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evaluate ∫ 1 / 1 – cos x dx

evaluate
∫  1 / 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 \frac{1}{1-cosx}dx
I = \int \frac{1+cosx}{(1-cosx)(1+cosx)}dx
I = \int \frac{1+cosx}{(1-cos^2x)}dx
I = \int \frac{1+cosx}{sin^2x}dx
I = \int (cosec^2x+cosecx.cotx)dx
I = \int cosec^2xdx+\int cosecx.cotxdx
I = -cotx+\int cosecx.cotxdx
I = -cotx-cosecx.cotx+c

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