Question

integral of cos^2x-sin^2x​

Answer 1

Answer:

(1/2)*sin 2x+c

Step-by-step explanation:

We have to find the integral of y = (cos x)^2 - (sin x)^2.

We know that cos 2x = (cos x)^2 - (sin x)^2

=> y = cos 2x

Int[ cos 2x dx]

let 2x = y, dy/2 = dx

=> Int[(1/2)cos y dy]

=> (1/2) sin y + C

substitute y = 2x

=> (1/2)*sin 2x + C

The required integral is (1/2)*sin 2x + C

Answer 2

Answer:

To find the integral of cos^2x-sin^2x. We know that cos^2x-sin^2x = cos2x. => Int (cos^2x-sin^2x) dx = (1/2)sin2x+C. The requested integral of the difference (cos x)^2 - (sin x)^2 is: Int [(cos x)^2 - (sin x)^2] dx = 2sin(x/2) + C.

Hope it is helpful and mark it as a brainlis tt