how do you simplify
[tex] \frac{ \sin(90 - \alpha ) \times \tan( - \alpha ) \times \cos( \alpha - 180) }{ \ \cos(100) \sin(135?) } [/tex]

Answers

Answer 1

Answer:

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{\sqrt{2} \times sin(2 \times \alpha) }{2 \times cos(100^{\circ}) }[/tex]

Explanation:

The given expression is presented as follows;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})}[/tex]

The sine, cosine, and tangent of the common angles are given as follows;

sin(A - B) = sin(A)·cos(B) - cos(A)·sin(B)

∴ sin(90° - α) = sin(90°)·cos(α) - cos(90°)·sin(α) = cos(α)

tan(-α) = -tan(α)

cos(A - B) = cos(A)·cos(B) + sin(A)·sin(B)

∴ cos(α - 180°) = cos(α)·cos(180°) + sin(α)·sin(180°) = -cos(α)

sin(135°) = sin(90° + 45°) = sin(90°)·cos(45°) + sin(45°)·cos(90°) = cos(45°) = √2/2

Therefore, we get;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times -cos( 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{cos( \alpha) \times -tan (\alpha) \times -cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}}[/tex]

[tex]\dfrac{cos( \alpha) \times -\dfrac{sin(\alpha)}{cos(\alpha)} \times -cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}} = \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}} = \dfrac{2}{\sqrt{2} } \times \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) }[/tex]

[tex]\dfrac{2}{\sqrt{2} } \times \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) } = \dfrac{sin(2 \times \alpha) }{\sqrt{2} \times cos(100^{\circ}) }[/tex]

Therefore;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{\sqrt{2} \times sin(2 \times \alpha) }{2 \times cos(100^{\circ}) }[/tex]


Related Questions

can you plz answer me from the photo​

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A. True
B. False
C. True

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Công nghệ đã thay đổi cách mọi người sử dụng để giao tiếp ở nơi làm việc hiện đại

If you see rough patches, loose,gravel,or potholes on the road you should

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Answer:

move out of the way

Explanation:

Drive around them in the safest way as possible. if that is not an option then turn around in a nearby parking lot of some sort and take another road to your destination

What is market information?

please answer in your own words since my teacher will probably notice if I plagerize

Answers

Answer:

Market information is is the understanding of the trends going on in a market such as demographic popular product age interests things like that

Explanation:

how is a trade off best described ?

dilema
compromise
demand
complication

Answers

I think the answer is compromise <3

Write a structured algorithm that prompts the
user to input two numbers. The algorithm should
multiply both numbers and then prompt the
user to enter the answer. The algorithm should
compare the answer entered with that calculated
and output "correct answer" or "incorrect answer"
accordingly. At the start, input how many sums
will be done.

Answers

Answer:

Step 1 : Start

Step2 : Input first number, num1

Step3 : Input second number, num2

Step4 : product - - > num1 * num2 (product of num1 and num2)

Step5 : Input product, myanswer

Step6 : comparison - - - > correct or incorrect based on myanswer and product

Step6: print(comparison)

Step7: End

Explanation:

Algorithm is a sequence of instructions a computer is expected to follow to solve a particular problem.

Required :

Two inputs ; num1 and num2

Expected output

Algorithm :

Step 1 : Start

Step2 : Input first number, num1

Step3 : Input second number, num2

Step4 : product - - > num1 * num2 (product of num1 and num2)

Step5 : Input product, myanswer

Step6 : comparison - - - > correct or incorrect based on myanswer and product

Step6: print(comparison)

Step7: End

The two numbers to multiply are entered ; the product is calculated by the program ; the the user inputs his or her own expecteted product ;

Both are compared and the output of the comparison is displayed (either correct oe incorrect)

Which scenario would most benefit from a self-join query?
a. a query connecting customers and products
b. a query connecting supervisors and customers
c. a query connecting employees and their orders
d. a query connecting employees and their supervisors

Answers

Answer:

answer is D

Explanation:

Just did it on edge

A current divider is to be designed using a 2mA DC current source and 1K resistors, the specification that the current is 1.5mA.

Answers

Answer:

The solution of the given query is described below throughout the explanation segment.

Explanation:

Given:

DC current,

= 2mA

Resistors,

= 1K

According to the question,

⇒ [tex]i=\frac{(1K+1K+1K)\times 2mA}{1K+1K+1K+1K}[/tex]

⇒   [tex]= \frac{3}{4}\times2mA[/tex]

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write a program to enter RADIUS of a CIRCLE and PRINT AREA of TRIANGLE using Q Basic. (class 8)​

Answers

Answer:

The program is as follows:

10 INPUT RADIUS, BASE, HEIGHT

20 CIRCLE = 3.142* RADIUS * RADIUS

30 TRIANGLE = 0.5* BASE * HEIGHT

40 PRINT CIRCLE

50 PRINT TRIANGLE

60 STOP

Explanation:

The program description doesn't tally;

In other words, it is impossible to calculate the area of a triangle using the radius of a circle.

So, I designed the program to get input for radius, base and height.

Get input for radius, base and height

10 INPUT RADIUS, BASE, HEIGHT

Calculate area of circle

20 CIRCLE = 3.142* RADIUS * RADIUS

Calculate area of triangle

30 TRIANGLE = 0.5* BASE * HEIGHT

Print area of circle

40 PRINT CIRCLE

Print area of triangle

50 PRINT TRIANGLE

End of program

60 STOP

Two use of dovetail saw

Answers

Answer:

They are particularly use when it is use for cutting small or very precise cut. They are particularly use in joint making mostly dovetail joints

hope it helps

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Answers

Answer:

Here is your answer

Explanation:

1. pick up litter and throw it away in a garbage can.

2. use environmentally household products such as washing powder, household cleaning agents

3. wash your car or outdoor equipment where it can flow to a gravel or grassed area instead of a street.

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Easy to install
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Answers

Answer:

Has a central powerful computer

Explanation:

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Answers

Answer:

Cable ties

Explanation:

Used to bundle cables neatly inside and outside of a computer. It is used to hold screws, jumpers, fasteners, and other small parts and prevent them from getting mixed together.

>3

[tex]\boxed{Parts\: organizer}[/tex] is used to hold screws, jumpers, fasteners, and other small parts and prevent them from getting mixed together.

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

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Answers

Answer:

JOHN NAPIER

Explanation:

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Answer:

Joost Bürgi

Explanation:

He invented it but John Napier worked on it earlier than Bürgi.

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Answers

Answer:

prfesssional education is any programs that improve the knowledge,skills and attitudes.

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Answer:

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Answer:

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Answers

Answer:

True

Explanation:

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O banded columns

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O borders

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Answers

Which is an example of a table style option?

O banded columns

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

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Answers

Answer:

metropolitan area network (MAN)

Explanation:

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On the other hand, a metropolitan area network (MAN) spans a geographic area like a city, is larger than a local area network (LAN) and smaller than wide area network (WAN).

Basically, a metropolitan area network (MAN) is formed by an aggregation of multiple local area network (LAN) that are interconnected using backbone provided by an internet service provider (ISP). A metropolitan area network (MAN) spans for about 5 kilometers to 50 kilometers in size.

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Answers

Answer:

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Explanation:

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Answers

Cell formats because I took it aboit 5 times and that was the answer so yeah

Answer:

I think choose (2)

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Answers

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Answers

Answer:

Following are the responses to the given question:  

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Answer:

put: forgot password to reset it

Answer:

Change your pass word

Open your Go ogle Account. You might need to sign in.

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Choose Password. You might need to sign in again.

Enter your new password, then select Change Password.

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Answer:

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Answers

Answer:

Part A

Adobe Dreamweaver is a computer application used for building websites and other types of web development, as well as mobile content development for both the intranet and the internet, on the Apple OS X and Windows Operating System Platforms

Part B

Adobe Dreamweaver is used for designing, building, and coding websites and mobile contents by developers and designers and by mobile content developers

Part C

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Explanation:

17.35 ma of current is flowing though a brown-red-brown resistor,what is v

Answers

Answer:

2.1V

Explanation:

brown-red-brown = 120Ω

V = I·R = 17.35 · 120 = 2.082V

However, the tolerance of the resistor is at least 10%, so you can't express the voltage that accurate.

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Answers

Answer:

Tell the teacher that you will pee in her coffee cup if they don't forget about what you did

Explanation:

Answer:

Explanation:

Depends on the homework, but

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>What is the output of the following code:

list1 = [ 'cyber', 786 , 2.23, 'square', 70.2 ]
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Answers

Answer:

Given code output is "786".

Explanation:

Code:

list1 = [ 'cyber', 786 , 2.23, 'square', 70.2 ]#defining a list list1 that holds value in parameter

print (list1[1] )#use a print method that prints list index value

In the given code a list "list1" is declared that holds value in it and in the next step a print method is declared that prints the first index value of the list.

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