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Grade 12Integral Calculus

evaluate
∫ cos x / 1 – cos x dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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