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$Evaluate \int_{- π / 2}^{π / 2} \log (\frac{a - \sin θ}{a + \sin θ}) d θ, a > 0 .$

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Correct option is A

f(θ)=log⁡a−sin⁡θa+sin⁡θf(−θ)=log⁡a+sin⁡θa−sin⁡θ=−log⁡a−sin⁡θa+sin⁡θ=−f(θ)since the integrand is an odd function the given integral is zero.

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Evaluate ∫−π/2π/2 log⁡a−sin⁡θa+sin⁡θdθ,a>0.

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$Evaluate \int_{- π / 2}^{π / 2} \log (\frac{a - \sin θ}{a + \sin θ}) d θ, a > 0 .$