Simplify (sin(theta))/(csc(theta))

Problem

sin(θ)/csc(θ)

Solution

1. Identify the trigonometric identity for the cosecant function.

csc(θ)=1/sin(θ)

2. Substitute the identity into the original expression.

sin(θ)/1/sin(θ)

3. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

sin(θ)⋅sin(θ)

4. Apply the exponent rule for multiplication.

sin2(θ)

Final Answer

sin(θ)/csc(θ)=sin2(θ)

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