If sinx + sin^2x = 1 then, show that cos^12x + 3cos^10x + 3cos^8x + cos^6x = 1

Answers

Answer 1

This can be proved by using identities of trigonometry.

Prove that cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1:

Given that,  

sin x + sin²x = 1 ⇒ sin x = 1 - sin²x

⇒ sin x = cos²x   (∵sin²x + cos²x = 1)

We have to prove that,

cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1

LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x

= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x

= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³

= (sin²x + sin x)³           (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)

= 1³ = 1 = RHS

LHS = RHS

Hence the equation is proved since both sides of the equation are equal.

Learn more about trigonometric identities here:

brainly.com/question/1979770

#SPJ4


Related Questions

Giselle's as a wallet containing four $5 bills, five $10 bills and three $20 bills. She pulls out two bills, one at a time without the first bill being returned to the wallet. Find the probability that both bills that she pulls out will be $5 bills.

Answers

Answer:

the answer is 4/12

Step-by-step explanation:

Here is an inequality: -x > 18. List some values for x that would make this inequality true.

Answers

Answer:

some examples x could equal:

x = -19

x = -20

x = -50

x = -100

so on

Step-by-step explanation:

remember negative x negative = positive

so any negative value beneath -18 will satisfy this because it will turn positive when multiplied by that outer minus sign.

hope this helped

help????????????????????​

Answers

Answer:

x=11

Step-by-step explanation:

12x+2 and 2x+112 are opposite exterior angles so they are congruent

Answer:

x=11

Step-by-step explanation:

12x + 2 and 2x + 112 are vertical angles meaning that they are equal to each other so we set up an equation that says 12x + 2 = 2x + 112 and solve for x

12x+2=2x+112

step one subtract 2 from each side

12x=2x+112

step 2 subtract 2x From each side

10x=110

step three divide each side by 10

x=11

Every time Kristina bakes a batch of brownies, she uses 1/8
a cup of chocolate. If she has 3/4
cup(s) of chocolate remaining, how many batches of brownies can Kristina make?

Answers

Answer:

6 batches

Step-by-step explanation:

3/4 divided by 1/8 = 6/8 divided by 1/8 = 6 batches

Lcm of deno ( 4, 8 ) = 8

3x2/4x2 = 6/8. 3/4 = 6/8

Kristina can make 6 batches of brownies

Write the equation of the line that passes through the points (1,4) and (1,-3).
y = -7x+11
X=1
y = 7x - 3

Answers

x=1
if you try and find the gradient which is change in y/ change in x so 7/0 you get 0 (no gradient). And it can’t be y= 1 as the y values are 4 and -3

A square cake sits on a circular cake stand. The circular cake stand has a diameter of 24 inches. The cake measures 16 inches on each side. How many square inches of the cake stand are visible?

Answers

Answer:

196.12 in^2

Step-by-step explanation:

circular cake stand area=(24/2)^2(3.14)=452.12 in^2

square cake=16x16=256 in^2

452.12-256=196.12 in^2

Solve each inequality for the variable. Show your work. 3x-7>4x+2

Answers

Step-by-step explanation:

3x-4x>2+7

-x>9

x>-9

Plz mark me as a brainlist

Simplify.

6⁴


simplify that

Answers

Answer= 6^2

Step by step: when the coefficient of the power is the same number, it has different rules so for division it’s just subtracting the powers which are 4-2

Answer:

6⁴/4²

Since, a^m/a^n = a^m-n

→ 6^4-2

→ 6^2

→ 6*6 = 36 Ans.

The question is in the picture

Answers

Answer:

(8, - 7)

Step-by-step explanation:

Since, (8, 7) is reflecting over x-axis, so after reflection, x- coordinate will remain same and y-coordinate changes from 7 to -7.

Therefore,

[tex] J(8,\: 7) \rightarrow J'(8,\: - 7)[/tex]

Answer:

-8,7 is the ans of the question

What is the slope of the line that passes through these two points (15,20) and (20,25)

Answers

Answer:

The slope Is 1.

Step-by-step explanation:

If you graph the two points it shows that the graph is done.

Answer:

slope = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (15, 20) and (x₂, y₂ ) = (20, 25)

m = [tex]\frac{25-20}{20-15}[/tex] = [tex]\frac{5}{5}[/tex] = 1

Which properties justify the steps taken to solve the system? {2a+7b=03a−5b=31 10a+35b=0; 21a−35b=217 ​31a = 217 a = 7 2(7)+7b=0 14 + 7b = 0 7b=−14 b=−2 what are each of the steps taken?

Answers

9514 1404 393

Explanation:

2a+7b=0 . . . . . . . . given [eq1]

3a−5b=31 . . . . . . . .given [eq2]

10a+35b=0 . . . . . . multiplication property of equality 5×[eq1] = [eq3]

21a−35b=217 ​. . . . .multiplication property of equality 7×[eq2] = [eq4]

31a = 217 . . . . . . . . addition/substitution properties of equality [eq3]+[eq4]

a = 7 . . . . . . . . . . . . division property of equality (÷31)

2(7)+7b=0 . . . . . . . .substitution property of equality; a=7 in [eq1]

14 + 7b = 0 . . . . . . . properties of real numbers

7b=−14 . . . . . . . . . . addition property of equality; add -14

b=−2 . . . . . . . . . . . . division property of equality (÷7)

Help If the side lengths of a cube are 16 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?

16 ⋅ 3
16 ⋅ 16 ⋅ 16
163
316

Answers

16 • 16 • 16! :)) hope this helped

Answer: I believe the answer is 6.3 I will research more and get a definite answer just dam me for the answer!

Step-by-step explanation:

:)

WILL GIVE BRAINLIEST!!!!!!!

2(x+1)^2=12

Answers

Answer:

Step-by-step explanation:

Zoltan read 15 pages of his book in 6 minutes. At this rate, how many pages can he read in 10 minutes?

Answers

Answer:

25 pages in 10 minutes.

The six sided of number cube are labeled 1,2,3,4,5 and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on heads and roll a number greater than 2?​

Answers

heads = 1/2

>2 = 2/3

2/3 x 1/2 = 1/3

Answer:

1 / 3

Can someone help me on this is for today pls!!!

Answers

Answer:

C

Step-by-step explanation:

The answer must be in square inches, not inches, so a and b are automatically wrong.

Couple of ways of doing it - the large triangles are congruent, so the area of each is the same. Since the area of a triangle is 1/2 base times height, the area of the 2 large triangles is just base times height, which is 18 * 11 or 198

Same principle for the smaller triangles at the top, area is 8 times 11, or 88. Add them up, you get 286 sq inches.

y=3x+−7

Find the slope.


A. 7




B. -7


C. 3x


D. 3

Answers

Answer:

D.3

Step-by-step explanation:

In the equation for a line in the form y=mx+c, m represents the slope.

Therefore the slope is 3.

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + - 7 ← is in slope- intercept form

with slope m = 3

Find the equation of the line which passes through (0,8) and (1,12)

Answers

Answer:y =4x + 8

Step-by-step explanation:

X-0/0-1 = y-8/8-12

Or,-4x = -y +8

So, y-4x = 8

Find the midpoint of the line segment from (4,5) to (-4,4)

Answers

9514 1404 393

Answer:

  (0, 4.5)

Step-by-step explanation:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

  ((4, 5) +(-4, 4))/2 = (4-4, 5+4)/2 = (0, 9)/2 = (0, 4.5)\

The midpoint is (0, 4.5).

-2(6) + 3(5 – 4​· ​2)

Answers

Answer:

-21

Step-by-step explanation:

-21. First multiply -2 and 6 to get -12. Then use order of operations to simplify the second parenthesis. 4•2 is 8. 5-8 is -3. 3(-3) = -9. Combine the two to get -21. Hope that helps!

Whos HAPPYYYYY today

Answers

Answer:

meeeeeeeeeeee super happy

Help me PLEASE! I will give Brainliest to the first correct answer.

Jada’s dog was 5 and 1/2 inches tall when it was a puppy. Now her dog is 14 and 1/2 inches taller than that. How tall is Jada’s dog now?

Answers

Answer:

20 inches tall

Step-by-step explanation:

First, I did 1/2+1/2=1. Then, I did 5+14=19. So, 19+1=20.

PROBLEM SOLVING A math club is having a bake sale. Find the area of the bake sale sign
TT IS
SWEET!
412ft
Math Club Baka Ina this Saturday
729 ft
The area of the sign is square feet.

Answers

The area of the bake sale sign is 6 ft²

Area

Area is the amount of space occupied by a two dimensional object.

Rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel.

The area of a rectangle = length * breadth

The area of the bake sale sign = length * breadth = [tex]\sqrt{4} *\sqrt[6]{729} = 6\ ft^2[/tex]

Find out more on Area at: https://brainly.com/question/25689052

Find the value of x in the following figure.

Answers

Answer:

x = 8

Step-by-step explanation:

180-(89+57)= 180-146 = 34

(5x -6) = 34

5x = 34 + 6

5x = 40

x = 40 ÷ 5

x = 8


Choose SSS, SAS, or AA to prove
the triangles are similar.

A. SSS
B. SAS
C. AA

Answers

Question :

Choose SSS, SAS, or AA to prove the triangles are similar.

A. SSS

B. SAS

C. AA

Answer :

As, all sides are given so we can use SSS to prove the triangles are similar.

So, correct option is A.

Explanation :

Given :

Sides of 1st triangle = 24, 32 and 40Sides of 2nd triangle = 27, 36 and 45

To Prove :

Triangles are similar

Proof :

As, all three sides are given so let's check ratio of all three sides.

1. [tex] \tt \cancel{\dfrac{24}{27}} = \dfrac{8}{9}[/tex]

2. [tex] \tt \cancel{\dfrac{32}{36}} = \dfrac{8}{9}[/tex]

3. [tex] \tt \cancel{\dfrac{40}{45}} = \dfrac{8}{9}[/tex]

As, all sides are in equal ratio.

So, by SSS

∆1 ~ ∆2

pls help me plssssss

Answers

Answer:

1

Step-by-step explanation:

It's the correct spelling.

Answer 1 is correct but this is under the wrong category

At a certain store a half gallon jug of milk cost 2.95 and a gallon jug of milk costs 5.95. Which milk has cheaper price?

Answers

Answer:

The first milk

Step-by-step explanation:

2.95 × 2 = 5.90

The first milk has cheaper price.


There are (2^6)^3• 2^0bacteria in a sample. What is the total number of bacteria in the sample?

Answers

Answer:

262,144

Step-by-step explanation:

2^0 = 1

(2^6)^3 = 2^18 = 262,144

Answer: 262,144.

Step-by-step explanation: (26)3(20)

=(643)(20)

=262144(20)

=(262144)(1)

=262144

Número de departamento vendidos en un edificio cualitativa o cuantitativa.​

Answers

Answer:The nucleus / large central vacuole contains

genetic material of a eukaryotic cell.

Step-by-step explanation:The nucleus / large central vacuole contains

Select the correct answer.
Identify the vertex of the function graphed below.


A.
(0,-2)
B.
(3,1)
C.
(1,1)
D.
(2,2)

Answers

Answer:

I think the answer is B

Step-by-step explanation:

Answer:

think it d

Step-by-step explanation:

because when i pick (3,1) it was wrong so that why it think it D

Other Questions
find the value for the following Which group did the United States eventually side with in World War I?A. only BritainB. the triple ententeC. the triple allianceD. the ottoman empire Let a and b be positive integers such that the product of all positive divisors of a equals the product of all positive divisors of b. Prove that a The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers Post-operative appointments should be approximately __________ in length. Find the area of the rhombus.9 m9 m9 m9 m Solve the following:-5 + 10(2 (-5) 3) + 3Give your answer in simplest form. When a person is standing upright, the weight of anything being lifted and carried in the hands is first reflected onto the: 9. Construct Arguments Write a two-columnproof for the Angle Bisector Theorem. MP.3 as mikayla prepares for her day, she reflects on her career choice as an esthetician. according to the text, her profession is particularly rewarding in that it allows her to help others feel good and make a positive impact on their The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as1L-10log where lo-10-12and is the least intense sound a human ear can hear. What is the approximate loudnessof a dinner conversation with a sound intensity of 10-7? Select the correct text In the passage.Whichthree sentences in this excerpt from Franklin D. Roosevelt's "Day of Infamy" speech make an emotional appeal by suggesting thatAmerica's Innocence was betrayed by certln enemies?Japan has,therefore, undertaken a surprise offensive extending throughout the Paclfic area. The facts of yesterday speak for themselves. Thepeople of the Unlted States have already formed their opinions and well understand the implications to the very life and safety of our nation.As Commander-In-Chlef of the Army and Navy, I have directed that all measures be taken for our defense.Always will we remember the character of the onslaught against us. No matter how long it may take us to overcome this premeditated invaslon,the American people in their righteous might will win through to absolute victory.I belleve I Interpret the will of the Congress and of the people when I assert that we will not only defend ourselves to the uttermost but will makevery certaln that this form of treachery shall never endanger us again.Hostilities exist. There is no blinking at the fact that our people, our territory and our interests are in grave danger.With confidence It our armed forces - with the unbounded determination of our people - we will galn the inevitable triumph so help us God.I ask that the Congress declare that since the unprovoked and dastardly attack by Japan on Sunday, December Seventh, 1941, a state of war hasexisted between the United States and the Japanese Empire.Reset Mrs. jones has been throwing up for several days, unable to eat or drink. you find her in bed. she is pale, lethargic, and her eyes are dull. she is likely suffering from:_______ 1. Answer the questions below to help you write your case summary. 2. Use the scroll bar on the right to move down the page. Criminal Charges What are the suspects accused of doing Company B is setting up commercial printing services on their network. Which of these are advantages of centrally managed commercial printers 22. What is the area of minor sector DFE?79.3 square cm15.2 square cm37.9 square cm66.1 square cm Avis needs some relief from the responsibilities of providing care for her husband. the social workers at aging alternatives indicates that she will most likely locate respite care through ______. What are the answers to quick check for 13-2 equivalence with customary units of capacity in savvas 4. (a)(i)Show that log4x=2log16x. (ii)Show that log x=3logb x. (iii) Show that logx=(1+log3)logix. five fundamental economic problems