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.
\[
\sin \alpha(\csc \alpha-\sin \alpha)
\]
\[
\sin \alpha(\csc \alpha-\sin \alpha)=
\]

Answer

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Answer

Final Answer: $\boxed{\cos^2 \alpha}$

Steps

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: $\boxed{\cos^2 \alpha}$