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$\int_{- π / 2}^{π / 2} \log (\frac{2 - \sin θ}{2 + \sin θ}) d θ$

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Correct option is A

f(θ)=log⁡2−sin⁡θ2+sin⁡θ⇒f(−θ)=log⁡2+sin⁡θ2−sin⁡θf(−θ)=−log⁡2−sin⁡θ2+sin⁡θf(−θ)=−f(θ)∴f(θ) is odd ∴∫−π/2π/2 f(θ)dθ=0

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∫−π/2π/2log2−sinθ2+sinθdθ

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$\int_{- π / 2}^{π / 2} \log (\frac{2 - \sin θ}{2 + \sin θ}) d θ$