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

1−cos⁡2x1+cos⁡x \frac{1-\cos ^{2} x}{1+\cos x}

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Full solution

Q. 1−cos⁡2x1+cos⁡x \frac{1-\cos ^{2} x}{1+\cos x}
  1. Recognize identity: Recognize the identity used in the numerator.\newlineUsing the Pythagorean identity, 1−cos⁡2(x)=sin⁡2(x)1 - \cos^2(x) = \sin^2(x).\newlineCalculation: Replace 1−cos⁡2(x)1 - \cos^2(x) with sin⁡2(x)\sin^2(x).
  2. Apply Pythagorean identity: Simplify the expression using the substitution.\newlineSubstitute into the original expression: (sin⁡2(x))/(1+cos⁡(x))(\sin^2(x))/(1 + \cos(x)).\newlineCalculation: (sin⁡2(x))/(1+cos⁡(x))(\sin^2(x))/(1 + \cos(x)).
  3. Simplify using substitution: Check for further simplifications or factorizations.\newlineNo further simplification or factorization is possible without additional constraints on xx.\newlineCalculation: None needed here.

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