Prove that `(sin theta+cos theta)(1-sin theta*cos theta)=sin^(3)theta+cos^(3)theta`

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta

Prove that (1+sin theta-cos theta)/(1+sin theta+cos theta)=tan((theta)/(2))

If (sin theta+cos theta)/(sin theta-cos theta)=3 then sin^4 theta-cos^4 theta=

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

Prove that :(sin5 theta+sin3 theta)/(cos5 theta+cos3 theta)=tan4 theta

Prove that :(1+sin theta-cos theta)/(1+sin theta+cos theta)=tan backslash(theta)/(2)

Prove that (cos theta)/(1+sin theta)=(1-sin theta)/(cos theta)=sec theta-tan theta

Prove that :(sin theta)/(cos(3 theta))+(sin3 theta)/(cos9 theta)+(sin9 theta)/(cos27 theta)=(1)/(2)(tan27 theta-tan theta)

Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)).