Simplify

Problem

sin(θ)/√(,1−sin2(θ))

Solution

1. Identify the trigonometric identity for the denominator. Recall the Pythagorean identity sin2(θ)+cos2(θ)=1

2. Rearrange the identity to solve for the expression under the square root.

cos2(θ)=1−sin2(θ)

3. Substitute the identity into the original expression.

sin(θ)/√(,cos2(θ))

4. Simplify the square root in the denominator, assuming cos(θ)>0 for the principal value.

sin(θ)/cos(θ)

5. Apply the quotient identity for tangent.

tan(θ)

Final Answer

sin(θ)/√(,1−sin2(θ))=tan(θ)

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