$\operatorname{cosec} 2 \theta-\cot 2 \theta=$

$\operatorname{cosec} 2 \theta-\cot 2 \theta=$
  1. $\tan \theta$
  2. $\sin 2 \theta$
  3. $\cos \theta$
  4. $\tan 2 \theta$

Solution

$\begin{aligned} \operatorname{cosec} 2 \theta-\cot 2 \theta &=\frac{1}{\sin 2 \theta}-\frac{\cos 2 \theta}{\sin 2 \theta} \\ &=\frac{1-\cos 2 \theta}{\sin 2 \theta}=\frac{2 \sin ^{2} \theta}{2 \sin \theta \cos \theta}=\tan \theta \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 1)

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