Differentiate $\displaystyle tan^{-1}(cos x)$ and hence evaluate $\displaystyle \int_0^\pi sin \frac{dx}{(2-sin^{2}x)}$
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Originally Posted by nerdzor Differentiate $\displaystyle \tan^{-1}(\cos x)$ and hence evaluate $\displaystyle \int_0^\pi {\color{red}\sin x} \frac{dx}{(2 - \sin^{2}x)}$ You have a made a typo (see the red). Can you differentiate the given function? Note that $\displaystyle 1 + \cos^2 x = 2 - \sin^2 x$ using the Pythagorean Identity. So the derivative of the function is equal to the integrand. What does that tell you ....?
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