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Integral Calculus> evaluate ∫ 1 / 1 – cos x dx...

question mark

evaluate
∫ 1 / 1 – cos x dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 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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