" 5."sin^(5)x*cos^(4)x

The number of solutions of the equation sin^(5)x-cos^(5)x=(1)/(cos x)-(1)/(sin x)(sin x!=cos x)

If /_\ = |[5+sin^(2)x,cos^(2)x,4sin2x],[sin^(2)x,5+cos^(2)x,4sin2x],[sin^(2)x,cos^(2)x,5+4sin2x]| =

Evaluate: int(cos^(4)x)/(sin^(3)x(sin^(5)x+cos^(5)x)^((3)/(5)))dx

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

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

The value of int(cos^(3)x+cos^(5)x)/(sin^(2)x+sin^(4)x)dx is

If (sin^(4)x)/(2)+(cos^(4)x)/(3)=(1)/(5), then

(i) int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx (ii) int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx (iii) int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx (iv) int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx (v) int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) dx

int ((4-5sin x) / (cos ^ (2) x) + (1) / (sin ^ (2) x cos ^ (2) x)) dx