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

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

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

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

Prove that 2sec^2theta-sec^4theta-2 cosec^2theta+cosec^4theta=cot^4theta-tan^4theta

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

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

Find sec^2 theta - 1/(cot^2 theta) . .

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

Prove the following (cos^2theta) /(1-tantheta) +sin^3theta/(sintheta-costheta) =1+sinthetacostheta

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) .