Q62 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

$$ \frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}= $$

  • A
    $2 \cos ^2 \theta$
  • B
    $-2 \cos ^2 \theta$
  • C
    $2 \tan ^2 \theta$
  • Correct answer
    D
    $2 \sec ^2 \theta$

Solution

$\begin{aligned} & \frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta} \\ & =\frac{1-\sin \theta+1+\sin \theta}{(1+\sin \theta)(1-\sin \theta)}=\frac{2}{1-\sin ^2 \theta}=\frac{2}{\cos ^2 \theta} \\ & =2 \sec ^2 \theta\end{aligned}$

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

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