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evaluate ∫ cosec x / cosec x – cot x dx

evaluate
∫  cosec x / cosec x – cot 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 \frac{cosecx}{cosecx-cotx}dx
I = \int \frac{\frac{1}{sinx}}{\frac{1}{sinx}-\frac{cosx}{sinx}}dx
I = \int \frac{1}{1-cosx}dx
I = \int \frac{1}{2sin^2\frac{x}{2}}dx
I = \int \frac{cosec^2\frac{x}{2}}{2}dx
I = \frac{-2cot\frac{x}{2}}{2}+c
I = -cot\frac{x}{2}+c

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