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Grade 12Integral Calculus

integrate the following integral
∫ 1 – 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

$I = \int \frac{1-cosx}{1+cosx}dx$
$I = \int \frac{2sin^{2}\frac{x}{2}}{2cos^{2}\frac{x}{2}}dx$
$I = \int tan^{2}\frac{x}{2}dx$
$I = \int (sec^{2}\frac{x}{2}-1)dx$
$I = \int sec^{2}\frac{x}{2}dx-\int dx$
$I = 2tan\frac{x}{2}-\int dx$
$I = 2tan\frac{x}{2}-x+c$

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