Verify the Identity sin(t)csc(t)=1

Problem

sin(t)*csc(t)=1

Solution

1. Identify the trigonometric identity for the cosecant function.

2. Substitute the definition csc(t)=1/sin(t) into the left side of the equation.

sin(t)⋅1/sin(t)

3. Simplify the expression by canceling the common factor of sin(t) in the numerator and the denominator.

sin(t)/sin(t)=1

4. Conclude that the left side equals the right side, verifying the identity.

Final Answer

sin(t)*csc(t)=1

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