Prove that `cos theta/(1-sin theta)=tan (pi/4+theta/2)`

Prove that cos (2theta) /(1+sin 2 theta)=tan(pi/4-theta)

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

Prove that cos((phi-theta)/2)-sinthetasin((phi+theta)/2)=costhetacos((phi+theta)/2)

If cos theta+sin theta=sqrt 2 cos theta ,then prove that cos theta-sin theta = sqrt 2 sin theta .

Solve 7 cos^2 theta+3 sin^2 theta=4

Prove that cos^2(pi/4-theta)-sin^2(pi/4-theta)=sin 2theta

Prove that sqrt((1-sin theta)/(1+sin theta))+sqrt((1+sin theta)/(1-sin theta))=-2/cos theta ,where pi/2ltthetaltpi .

Prove that (1+cosec theta -cot theta)/(1+cosec theta+cot theta)=(1-cos theta)/sin theta.

If tan theta = p/q , proved that (p sin theta -q cos theta)/(p sin theta+q cos theta) is (p^2-q^2)/(p^2+q^2) .

Prove that (sintheta-sin5theta+sin9theta-sin13theta)/(costheta-cos5theta-cos9theta+cos13theta)=cot4theta