Q71 / 150 · MHT CET 2021 (23 Sep Shift 1) · Mathematics

$\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$

  • Correct answer
    A
    0
  • B
    $4 \log 3$
  • C
    $\frac{1}{2}$
  • D
    $2 \log 4$

Solution

Figure
Eq. (1) $+(2)$ gives, $$ 2 I=\log \left[\frac{4+3 \sin x}{4+3 \cos x} \times \frac{4+3 \cos x}{4+3 \sin x}\right] d x=\int_0^{\frac{\pi}{2}}(\log 1) d x=0 $$

Hence, the correct answer is option: 'A'.

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