Problem
Write the expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of $\alpha$ only. \[ \sin \alpha(\csc \alpha-\sin \alpha) \] \[ \sin \alpha(\csc \alpha-\sin \alpha)= \]
Solution
Step 1 ：Given the expression \(\sin \alpha(\csc \alpha-\sin \alpha)\)
Step 2 ：Replace \(\csc \alpha\) with \(1/\sin \alpha\) to get \(\sin \alpha(1/\sin \alpha-\sin \alpha)\)
Step 3 ：Simplify the expression to get \(\cos^2 \alpha\)
Step 4 ：Final Answer: \(\boxed{\cos^2 \alpha}\)
