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

Prove that 1+cot^(2) theta = cosec^(2) theta

Prove that : 2 sin^2 theta + 4 cos (theta + alpha) sin alpha sin theta + cos 2 (alpha + theta) is independent of theta.

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

Prove that sin^2 theta+sin^2 2theta+sin^2 3theta+....+sin^2 n theta=n/2-(sin n theta cos(n+1)theta)/(2sin theta)

Prove that : sec^(2)theta+"cosec"^(2)theta=sec^(2)theta*"cosec" ^(2)theta

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

Prove that sqrt(sec^(2)theta + cosec^(2)theta) = tantheta + cottheta .