Question

If sin x + cos x =p then cos^2(2x) equals to what

Answer 1

ANSWER : cos^2 (2x) = p^2 (2 - p^2)

STEP BY STEP EXPLANATION :

We have,

sinx + cosx =p ---(1)

We know that,

sin^2 x + cos^2 x = 1 ----(2)

Thus, using the formula of (a^2 + b^2) =(a+b)^2 - 2ab, we get

(sinx +cosx)^2 - 2sinx.cosx =1

Substituting the value of eqn 1 in the above eqn, we get

p^2 -2sinx cosx = 1

We know,

2sinx.cosx= sin(2x)

p^2 - 1= sin(2x)

Using eqn 2 we get,

sin^2 (2x) +cos^2 (2x) =1

Thus,

(p^2 - 1)^2 + cos^2 (2x) =1

Thus,

cos^2 (2x) =1 - p^4 +2p^2 - 1

= 2p^2 - p^4

cos^2 (2x) = p^2 (2 - p^2)