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The value of $\int_{0}^{α} \frac{d x}{1 - \cos α \cos x} (0 < α < π / 2)$ is

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detailed solution

Correct option is D

Putting tan⁡x2=t the given integral reduces to=2∫0tan⁡α2 dt(1−cos⁡α)+t2(1+cos⁡α)=1cos2⁡α2∫0tan⁡α/2 dtt2+tan2⁡α2=1cos2⁡α2tan⁡α2tan−1⁡ttan⁡α20tanα⁡/2=1sin⁡α2cos⁡α2⋅π4=π2sin⁡α

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The value of ∫0α dx1-cos⁡αcos⁡x(0<α<π/2) is

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The value of $\int_{0}^{α} \frac{d x}{1 - \cos α \cos x} (0 < α < π / 2)$ is