Prove that `\sin \theta .\cosec \theta =1`.

Prove that, sin^2 theta+ cosec^2 theta>=2

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

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

Prove that : (sin theta + sec theta) ^(2) + (cos theta + cosec theta) ^(2) = (1 + sec theta cosec theta) ^(2).

Prove that : cosec theta + cosec 2 theta + cosec 2^2 theta +...........+cosec2^(n-1) theta= cot(theta/2)-cot 2^(n-1)theta

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .

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

Prove that cos^2 theta cosec theta+sin theta=cosec theta

Prove that : (sin^(4)theta- cos^(4) theta+ 1) "cosec"^(2)theta=2

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