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$If \int_{0}^{k} \frac{\cos x}{1 + \sin^{2} x} d x = \frac{π}{4} then k =$

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Correct option is C

∫0k dt1+t2=π4 put sin⁡x=t⇒tan−1⁡t0k=π4 cos⁡x⋅dx=dt⇒tan−1⁡(sin⁡x)0k=π4tan1⁡(sin⁡k)−tan−1⁡(sin⁡0)=π4tan−1⁡(sin⁡k)−0=π4⇒sin⁡k=1k=π2

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If ∫0k cos⁡x1+sin2⁡xdx=π4 then k=

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$If \int_{0}^{k} \frac{\cos x}{1 + \sin^{2} x} d x = \frac{π}{4} then k =$