" 15."(cos^(3)x-sin^(3)x)/(cos x-sin x)=(1)/(2)(2+sin2x)

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

int(3cos3x-2sin2x)/(cos2x+sin3x)dx

int (3 cos 3x-2 sin 2x)/(cos 2x+ sin 3x)dx=

tan^(-1)[(2cos x-3sin x)/(3cos x+2sin x)]

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) .

3-2cos x-4sin x-cos2x+sin2x=0

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

int(sin2x+sin5x-sin3x)/(cos x+1-2sin^(2)2x)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

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx