Compute the following: ` [[cos^2x, sin^2x],[sin^2 x, cos^2 x]]+[[sin^2x, cos^2 x],[cos^2 x, sin^2 x]]`

Solve (1+sin^2x-cos^2x)/(1+sin^2x+cos^2x)

If the maximum and minimum values of the determinant |(1 + sin^(2)x,cos^(2) x,sin 2x),(sin^(2) x,1 + cos^(2) x,sin 2x),(sin^(2) x,cos^(2) x,1 + sin 2x)| are alpha and beta , then

Evaluate the following integrals. int sin x cos x (sin 2x + cos 2x) dx

Evaluate the following integrals: int frac{sin^6x+cos^6x}{sin^2x cos^2x}dx

sqrt(sin 2x) cos 2x

Integrate the following: int{(5cos^3x+2sin^3 x)/(2sin^2 x*cos^2 x)+sqrt(1+sin2x)+(1+2sin x)/(cos^2x)+(1-cos2x)/(1+cos 2x)}dx

Solve 2 sin^(2) x-5 sin x cos x -8 cos^(2) x=-2 .

Evaluate: int \ (sin^2x cos^2x)/(sin^5x+cos^3x sin^2x + sin^3x cos^2x + cos^5x)^2 \ dx

If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)| is expanded in powers of sin x , then the constant term is

If sin x+sin^2=1 , then cos^8 x+2 cos^6 x+cos^4 x=