If θ = 2xy/x²-y² then what is cos θ equal to?

Correct Answer is : 2xyx2+y22xy/x²+y²x2+y22xy

Correct Answer is : 2xyx2+y22xy/x²+y²x2+y22xy

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Trigonometry Practice Test 2

Question : 1 of 22

Marks: +1, -0

\cot\theta = \frac{2xy}{x^2-y^2}

then what is cos θ equal to?

Solution:

Concept:

Use a right triangle to relate

\cot\theta

with

\cos\theta

Explanation:

Given

\cot\theta = \frac{2xy}{x^2-y^2}

Take the adjacent side as

2xy

and the opposite side as

x^2-y^2

Then hypotenuse is

\sqrt{(2xy)^2+(x^2-y^2)^2}

Simplify:

\sqrt{4x^2y^2+x^4-2x^2y^2+y^4}=\sqrt{(x^2+y^2)^2}

So hypotenuse

=x^2+y^2

Now

\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}

Thus

\cos\theta = \frac{2xy}{x^2+y^2}

Answer:

\cos\theta = \frac{2xy}{x^2+y^2}

Hence, option C is correct.

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