(cos x-sin x)^(2)=1-sin2

int(cos x+sin x)/(cos x-sin x)(1-sin2x)dx

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

if a=(1+sin x)/(1-cos x+sin x) then (1+cos x+sin x)/(2sin x) is

("sin x - cos x")^(2) =1- sin 2x

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

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

(d)/(dx)[(1+cos2x+sin2x)/(1+sin2x-cos2x)]=

Integration using trigonometric identities : int (cos^(8)x-sin^(8)x)/(1-2sin^(2)xcos^(2)x)dx=...+c

Prove that: (i) (1+"sin" 2theta-cos 2theta)/(1+"sin" 2theta+cos 2theta)="tan" theta . (ii) 2 tan 2x=(cos x+"sin" x)/(cos x-"sin" x)-(cos x-"sin" x)/(cos x+"sin" x) .