Answer
See explanations.
Work Step by Step
Step 1. $LHS=sin(t)cos(t)(\frac{sin(t)}{cos(t)}+\frac{cos(t)}{sin(t)})=sin^2t+cos^2t=1$
Step 2. $RHS=1$
Step 3. Since $LHS=RHS$, we verified the identity.
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