Problem

8. \( 3 \sin ^{3} t \csc t+\cos ^{2} t+2 \cos (-t) \cos t \)

Answer

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Answer

\( 3\sin^2 t + \cos^2 t + 2\cos^2 t = 3\sin^2 t + 3\cos^2 t \)

Steps

Step 1 ：\( 3\sin^3 t \csc t = 3\sin^2 t \)

Step 2 ：\( 2\cos(-t)\cos t = 2\cos^2 t \)

Step 3 ：\( 3\sin^2 t + \cos^2 t + 2\cos^2 t = 3\sin^2 t + 3\cos^2 t \)

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