" 24."(sin^(2)x)/(1+cos x)quad " 25."(cos x-cos2x)/(1-cos x)

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

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

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

int (sin x) / ((1-cos x) (2-cos x)) dx

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

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) .

(cos x)/(1-sin x)=(1+cos x+sin x)/(1+cos x-sin x)

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

lim_(x->0)(1-cos x-cos2x+cos x*cos2x)/(x^(4))