Question

5. If cosA = 2x/1+x^2,
then find the values of sinA and tanA in terms of x.
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Answer 1

Answer:

since cos A = 2x / 1+x^2

base / hypotenuse = 2x / 1 + x^2

Pythagoras theorem :

height^2 = hypotenuse ^2 - base^2

height^2 = (1 + x^2)^2 - (2x)^2

height^2 = 1 + x^4 - 2x^2

height = 1 + x^2 - (2x^2)1/2

sin A = (1 + x^2 - (2x^2)^1/2) / 1 + x^2

tan A = (1 + x^2 - (2x^2)^1/2) / 2x

Answer 2

I hope it is useful to you.