$\int_{0}^{\frac{π}{2}} \frac{sin x}{1 + {cos}^{2} x} d x$ .

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Solution

Putting $cos x = t$
$- sin x = d t$
$\int_{0}^{1} \frac{1}{1 + t^{2}} d t$
$[{tan}^{- 1} t]_{0}^{1}$
$⟹ \frac{π}{4}$

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