Using Pythagoras theorem, prove that 1 + `cot^2 theta = cosec^2 theta,`

Using Pythagoras theorem, prove that 1 + cot^2 theat = coses^2 theta ,

Prove that cot 2 theta + tan theta = cosec 2 theta

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

Prove that cosec 2alpha = cot alpha - cot 2alpha . Hence or otherwise prove that cosec theta + cosec 2theta + cosec 4theta + cosec 8theta = cot theta/2 - cot 8theta .

Prove the following identity : cosec^6 theta- cot^6 theta =3 cot^2 theta cosec^2 theta+1 .

show that 1 + (cot^2 theta/ (1 + cosec theta)) = cosec theta

cosec^(2)theta-cot^(2)theta-1

Prove that cot^4 theta+ cot^2 theta= cosec^4 theta-cosec^2 theta

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

cosec^2 theta - cot^2 theta = 1 +…..