Question

integration of 1-cosx\1+cosx

Answer 1

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Answer 2

Answer:

$→ \int \frac{1 - \cos(x) }{1 + \cos(x) } dx \\ = \int \frac{2 \sin^{2} ( \frac{x}{2} ) }{2 \cos^{2} ( \frac{x}{2} ) } dx \\ = \int \tan^{2} ( \frac{x}{2} ) dx \\ = \int (\sec^{2} ( \frac{x}{2} ) - 1) dx \\ = \int \sec^{2} ( \frac{x}{2} ) dx - \int dx \\ = \frac{ \tan( \frac{x}{2} ) }{ \frac{1}{2} } - x +C \\ = 2 \tan( \frac{x}{2} ) - x + C$

• 2tan(x/2)-x+C is the right answer.