If 3 sin x + 5 cos x = 5, show that 3 cos x - 5 sin x = `+- 3`.

Find the derivatives of: cos(a cos x + b sin x)

Show that the following pair of sets are equal A = {x :x is an integer such that .5 < x < 7.5} , B = {1, 2, 3, 4, 5, 6, 7}

If P(x) =[(cos x, -sin x),(sin x , cos x)] , then show that P(A) P(B)=P(A+B) .

Find the value of x such that cos (sin^(-1)x)=(1)/(2) .

Simplify tan^(-1) [(a cos x -b sin x)/(b cos x +a sin x)] , if (a)/(b) tan x gt -1 .

If 2 tan A = 3 tan B.show that tan (A - B)= (sin2B)/(5-cos2B)

If theta=30° , show that 3sin theta- 4sin^3 theta= sin theta cos2 theta + costheta sin 2theta .

If cos^4x/cos^2y+sin^4x/sin^2y=1 ,show that cos^4y/cos^2x+sin^4y/sin^2x=1

If f(x)=(5x+3)/(4x-5) , (x ne 5/4) show that f{f(x)} is a identity function.