Simplify (cos(x)^2)/(1-sin(x))

Problem

cos^2(x)/(1−sin(x))

Solution

1. Identify the Pythagorean identity for the numerator, which states that sin^2(x)+cos^2(x)=1

2. Substitute the identity cos^2(x)=1−sin^2(x) into the expression.

(1−sin^2(x))/(1−sin(x))

3. Factor the numerator using the difference of squares formula, a^2−b^2=(a−b)*(a+b)

((1−sin(x))*(1+sin(x)))/(1−sin(x))

4. Cancel the common factor (1−sin(x)) from the numerator and the denominator.

1+sin(x)

Final Answer

cos^2(x)/(1−sin(x))=1+sin(x)

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