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

Problem

1−sin2(x)/(1+cos(x))

Solution

1. Apply the Pythagorean identity to rewrite the numerator, using sin2(x)=1−cos2(x)

1−(1−cos2(x))/(1+cos(x))

2. Factor the numerator as a difference of squares, where 1−cos2(x)=(1−cos(x))*(1+cos(x))

1−((1−cos(x))*(1+cos(x)))/(1+cos(x))

3. Cancel the common factor of 1+cos(x) from the numerator and the denominator.

1−(1−cos(x))

4. Distribute the negative sign and simplify the expression.

1−1+cos(x)

cos(x)

Final Answer

1−sin2(x)/(1+cos(x))=cos(x)

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