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

Prove that (((1+cot theta +tan theta)(sintheta-costheta))/(sec^3theta -cosec^3theta)) = (sin^2theta cos^2theta)

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

lf 5 cos theta=7 sin theta , find the value of ( sin theta + cos theta)/(2 sin theta -3 cos theta) .

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

Evaluate (sin (90 - theta). cos (90 - theta))/(sin theta cos theta)

If theta=30° , show that 3sin theta- 4sin^3 theta= sin theta cos2 theta + costheta sin 2theta .

If 4 tan theta=3 , find the value of (4 sin theta-3 cos theta)/(4 sin theta+3 cos theta) .

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