If: `cos^(16)x - sin^(64)x =1`, then: x=

If y=(sin^(-1)x-cos^(-1)x)/(sin^(-1)x+cos^(-1)x)," then "(dy)/(dx)=

If sin x + sin^(2) x =1 " then " cos^(8) x + 2 cos^(6) x + cos^(4) x =

(cos^(3) x- sin^(2) x)/(cos x - sin x)=(1)/(2) (2 + sin 2x)

If x in (-pi, pi) such that y=1 +|cos x|+|cos^(2)x|+|cos^(3)|+ …. And 8^(y)=64 , then y =

2cosx-cos3x-cos5x= ............... A) 16 cos ^(3) x sin ^(2) x B) 16 sin^(2) x cos ^(2) x C) 4 cos ^(2) x sin ^(2) x D) 4 sin ^(2) x cos ^(2)x

Prove that cos ^(3) x sin ^(2) x = (1)/(16) (2cos x - cos 3x - cos 5x).

If f(x)={{:(sin(cos^(-1)x)+cos(sin^(-1)x)",",xle0),(sin(cos^(-1)x)-cos(sin^(-1)x)",",xgt0):} then at x = 0

int (sin^(-1) x -cos^(-1)x)/(sin^(-1) x + cos^(-1)x) dx =