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evaluate ∫ cot x / cosec x – cot x dx

evaluate
∫  cot 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{cotx}{cosex-cotx}dx
I = \int \frac{cotx(cosecx+cotx)}{(cosecx-cotx)(cosecx+cotx)}dx
I = \int \frac{cotx(cosecx+cotx)}{(cosec^2x-cot^2x)}dx
I = \int \frac{cotxcosecx+cot^2x}{1}dx
I = \int cotxcosecxdx+\int cot^2xdx
I = -cosecx+\int cosec^2xdx-\int dx
I = -cosecx-cotx-x+c

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