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

Show that tan (pi/4+theta/2)=sec theta +tan theta .

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

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

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

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

Simplify: tan theta[(sec theta, tan theta),(tan theta, -sec theta)] + sec theta[(- tan theta, -sec theta),(-sec theta, tan theta)] .

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

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

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