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evaluate the following integral ∫ sqrt{(1 – cos x) / (1 + cos x)} dx

evaluate the following integral
∫ sqrt{(1 – cos x) / (1 + cos x)} dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \sqrt{\frac{1-cosx}{1+cosx}}dx
I = \int \sqrt{\frac{2sin^{2}\frac{x}{2}}{2cos^{2}\frac{x}{2}}}dx
I = \int \frac{sin\frac{x}{2}}{cos\frac{x}{2}}dx
cos\frac{x}{2}=t
-sin\frac{x}{2}\frac{dx}{2}=dt
I = -2\int \frac{dt}{t}
I = -2log(t)+c
I = -2log(cos\frac{x}{2})+c
I = 2log(sec\frac{x}{2})+c

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