Question

sin(theta)csc(theta)-sin(90-theta)sec(theta)=0

Answer 1

\[\sin\theta\csc\theta-\sin(90-\theta)\sec\theta=0\]
Use the angle difference identity for sine:
\[\sin(x-y)=\sin x\cos y-\sin y\cos x\]
Also, recall that \(\displaystyle\frac{1}{\sin\theta}=\csc\theta.\)