int {{{tan }^{ - 1}}sqrt {frac{{1 - cos 2x}}{ | vedclass

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Question

(C) We know that $1 - \cos 2x = 2\sin^2 x$ and $1 + \cos 2x = 2\cos^2 x$. Substituting these into the integral: $\int {{	an ^{ - 1}}\sqrt {\frac{{2\s

Vedclass · Accepted Answer

$\frac{{{x^2}}}{2} + c$

Vedclass · Answer

(C) We know that $1 - \cos 2x = 2\sin^2 x$ and $1 + \cos 2x = 2\cos^2 x$. Substituting these into the integral: $\int {{	an ^{ - 1}}\sqrt {\frac{{2\sin^2 x}}{{2\cos^2 x}}} } \,dx = \int {{	an ^{ - 1}}\sqrt {	an^2 x} } \,dx$ $= \int {{	an ^{ - 1}}(	an x)\,dx} = \int x \,dx$ $= \frac{{{x^2}}}{2} + c$.

$\int {{{\tan }^{ - 1}}\sqrt {\frac{{1 - \cos 2x}}{{1 + \cos 2x}}} } \;dx = $

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