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eduard
3 years ago
5

True or false. Tan^2 x = 1 - cos2x/ 1 + cos 2x

Mathematics
1 answer:
koban [17]3 years ago
5 0

<u>ANSWER</u>

True

<u>EXPLANATION</u>

The given trigonometric equation is

\tan^{2} (x)  =  \frac{1 -  \cos(2x) }{1 +  \cos(2x) }

Recall the double angle identity:

\cos(2x)  =  \cos^{2} x -   \sin^{2}x

We apply this identity to obtain:

\tan^{2} (x)  =  \frac{1 - (\cos^{2} x -   \sin^{2}x) }{1 +  (\cos^{2} x -   \sin^{2}x) }

We maintain the LHS and simplify the RHS to see whether they are equal.

Expand the parenthesis

\tan^{2} (x)  =  \frac{1 - \cos^{2} x  +  \sin^{2}x }{1 +  \cos^{2} x -   \sin^{2}x}

\implies\tan^{2} (x)  =  \frac{1 - \cos^{2} x  +  \sin^{2}x }{1  -   \sin^{2}x  + \cos^{2} x }

Recall that:

1  -   \sin^{2}x  =  \cos^{2}x

1  -   \cos^{2}x  =  \sin^{2}x

We apply these identities to get:

\implies\tan^{2} (x)  =  \frac{\sin^{2}x +  \sin^{2}x }{\cos^{2} x + \cos^{2} x }

\implies\tan^{2} (x)  =  \frac{2\sin^{2}x }{ 2\cos^{2} x }

\implies\tan^{2} (x)  =  \frac{\sin^{2}x }{ \cos^{2} x }

\implies \tan^{2} (x)  =(  \frac{\sin x }{ \cos x })^{2}

Also

\frac{\sin x }{ \cos x } =  \tan(x)

\implies \tan^{2} (x)  =( \tan x )^{2}

\implies \tan^{2} (x)  =\tan^{2} (x)

Therefore the correct answer is True

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Given:

The inequality is

3|p+4|+5

To find:

The solution set for the given inequality.

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We have,

3|p+4|+5

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3|p+4|

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|p+4|

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The solution set of the given inequality is (-5,-3).

Therefore, the correct option is A.

7 0
2 years ago
At Costco, you can buy a ten-pound bag of Halloween candy for $23.99. Kroger is running a special on the same brand of candy: bu
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Answer:

A. 2.40

B. 4

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3 years ago
Find the output, k, when the input, t, is -7.<br><br> k= 10t - 19<br><br> k=
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3 years ago
A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find
natta225 [31]

The tension in the cable is given by the newton's first law will be 163.622 N.

<h3>What is newton's first law?</h3>

The summation of the force is equal to zero.

The formula is given as

ΣF = 0

Where m is the mass of the body and a is the acceleration.

A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam.

Then the tension in the cable will be

Let T be the tension in the cable.

T sin 29° + T sin 53° – 210 = 0

On simplifying, we have

T (sin 29° + sin 53°) = 210

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More about the newton's first law link is given below.

brainly.com/question/974124

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6 0
2 years ago
Alice has a total of 12 dimes and nickels. She has 2 more nickels than dimes
valkas [14]
This is a problem of system of linear equations in two variables. This concept of mathematics is very useful in real-life problems. You can solve a system by finding the solution. A solution of a system are the values of the variables that satisfies each equation in the system. So by knowing these concepts we can get a system of equation by analyzing each statement step by step, that is:

1. Alice has a total of 12 dimes and nickels.

Let the variables:

D: Dimes \\ N:Nickles

1st. Equation:

D+N=12

<span>2. She has 2 more nickels than dimes

2nd Equation:

N=D+2

Therefore our system of linear equations is:

</span>(1) \ D+N=12 \\ (2) \ N=D+2 \\ \\ Substituting \ (2) \ in \ (1): \\ D+(D+2)=12 \therefore 2D=10 \therefore D=5 \\ \\ Solving \ for \ N \ in \ (2): \\ N=5+2=7

Conclusion:

<span>Alice has 5 dimes and 7 nickels. </span>
6 0
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