Simplify (sin(x))/( square root of 1-sin(x)^2)

Problem

sin(x)/√(,1−sin2(x))

Solution

1. Identify the trigonometric identity for the denominator using the Pythagorean identity sin2(x)+cos2(x)=1

2. Substitute 1−sin2(x) with cos2(x) inside the square root.

1−sin2(x)=cos2(x)

3. Simplify the square root expression, assuming x is in a quadrant where cos(x) is positive, or expressing it generally as |cos(x)|

√(,cos2(x))=cos(x)

4. Apply the definition of the tangent function, which is the ratio of sine to cosine.

sin(x)/cos(x)=tan(x)

Final Answer

sin(x)/√(,1−sin2(x))=tan(x)

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