Question

How do you solve sec/sinx -sinx/cosx=cotx

Answer 1

solve? or prove?

Answer 2

\[\begin{align*}\frac{\sec x}{\sin x}-\frac{\sin x}{\cos x}&=\frac{1}{\cos x\sin x}-\frac{\sin x}{\cos x}\\\\
&=\frac{1}{\cos x\sin x}-\frac{\sin^2x}{\sin x\cos x}\\\\
&=\frac{1-\sin^2x}{\cos x\sin x}\\\\
&=\frac{\cos^2x}{\cos x\sin x}\\\\
&=\frac{\cos x}{\sin x}\\\\
&=\cot x
\end{align*}\]