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

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

Prove that (tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta

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

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

If sec theta+tan theta=(1)/(2) The value of sec theta=

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

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

Prove that 1 + tan 2 theta tan theta = sec 2 theta .

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

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