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evaluate ∫ cos x / 1 – cos x dx

evaluate
∫  cos x / 1 – cos x dx

Grade:12

1 Answers

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

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

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