cosec2 theta cosec theta identical cot2 theta1 sin thetaSo

cosec^2 theta - cosec theta identical cot^2 theta/1 + sin theta

Solution

Cosec²theta -cosec theta=cot²theta/(1+sin theta)

Starting with the right side

Cot²theta/(1+sin theta)

Cot²theta(1-sin theta)/(1+sin theta)(1-sin theta)

Cot²theta(1-sin theta)/(1-sin²theta)

Cot²theta(1-sin theta)/cos²theta

Cosec²theta(1-sin theta)

Cosec²theta-cosec²theta *sin theta

Cosec²theta-cosec theta