Prove that : `(cos theta)/(1-tan theta) + (sin theta)/(1-cot theta) = sin theta + cos theta`

Prove that (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta) = (sec theta cosec theta +1)

Prove that (costheta)/(1-sin theta)+(1-sin theta)/(cos theta)=2sec theta .

Prove that (sin 3 theta)/( sin theta) - (cos 3 theta)/(cos theta) = 2

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + sec theta cosec theta

Prove that : (sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta

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

Prove that cos theta (tan theta +2) (2tan theta +1) = 2 sec theta + 5 sin theta

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

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

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