Let `f(x)=|secxcosxsec^2x+cotxcos e cxcos^2xcos^2x cos e c^2x1cos^2xcos^2x|` Prove that `int_0^(pi/2)f(x)dx=-pi/4-8/(15)`

Prove that 1+cos2x+cos4x+cos6x=4cosxcos2xcos3x .

Prove that int_(0)^(pi)(xsin^(3)x)/(1+cos^(2)x)dx=pi/2(pi-2)

Prove that int_(0)^(pi/4)(sin2xdx)/(sin^(4)x+cos^4 x)=(pi)/(4)

Let f(x)=|2cos^2xsin2x-sinxsin2x2sin^2xcosxsinx-cosx0| . Then the value of int_0^(pi//2)[f(x)+f^(prime)(x)]dx is a. pi b. pi//2 c. 2pi d. 3pi//2

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Prove that: int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx = pi^2

Evaluate: int_(0)^(pi/2)(dx)/(4sin^(2)x+5cos^(2)x)