If `tan theta=a/b` then prove that `(bsec theta)/(a cosec theta)=1

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

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

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

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

Prove that (sin theta + cos theta )( cosec theta - sec theta ) = cosec theta. Sec theta -2 tan theta

Prove that: sin theta (1 + tan theta) + cos theta (1+ cot theta) = sec theta + cosec theta .

Prove that: sin theta(1+ tan theta) + cos theta (1+ cot theta) = sec theta + "cosec" theta

tan theta+(1)/(tan theta)=sec theta cosec theta

Prove the following identity : sqrt (sec^2 theta+ cosec^2 theta)= tan theta+ cot theta= sec theta cosec theta .

Prove that, (cot theta - tan theta)/(1-2 sin ^(2) theta) = sec theta "cosec" theta