If $\cot (A+B)=0$, then $\sin (A+2 B)$ is equal to

If $\cot (A+B)=0$, then $\sin (A+2 B)$ is equal to
  1. $\sin 2 A$
  2. $\cos A$
  3. $\sin A$
  4. $\cos 2 A$

Solution

$\cot (A+B)=0 \Rightarrow A+B=(2 n+1) \frac{\pi}{2} \Rightarrow B=(2 n+1) \frac{\pi}{2}-A$ Now, $\sin (A+2 B)=\sin (A+(2 n+1) \pi-2 A)$ $=\sin ((2 n+1) \pi-A)=\sin A$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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