Simplify cos(t)csc(t)

Problem

cos(t)*csc(t)

Solution

1. Identify the trigonometric identity for the cosecant function.

csc(t)=1/sin(t)

2. Substitute the identity into the original expression.

cos(t)⋅1/sin(t)

3. Multiply the terms to combine them into a single fraction.

cos(t)/sin(t)

4. Apply the quotient identity for the cotangent function.

cos(t)/sin(t)=cot(t)

Final Answer

cos(t)*csc(t)=cot(t)

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