Question

Prove that cos^2θ/sinθ-cosecθ+sinθ=0

Answer 1

this may help you my friend.

Answer 2

Here make use of the identity $1-\sin^2 x=\cos ^2x$.

$LHS=\frac{\cos^2 \theta}{\sin \theta - \csc \theta} +\sin \theta\\ LHS=\frac{\cos^2 \theta}{\sin \theta -\frac{1}{\sin \theta} } +\sin \theta \\ LHS=\frac{\cos^2 \theta \sin \theta}{\sin^2 \theta -1 } +\sin \theta \\ LHS=\frac{\cos^2 \theta \sin \theta}{-\cos^2 \theta } +\sin \theta \\ LHS=-\sin \theta +\sin \theta \\ LHS=0=RHS$

The proof is complete.