Solve: 2 x=- (x+ 3 ) - Vidyadip

Question

Solve: $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$

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Answer

Here we have, tan 2x = $-\cot \left(x+\frac{\pi}{3}\right)=\tan \left(\frac{\pi}{2}+x+\frac{\pi}{3}\right)$
or tan2x = $\tan \left(x+\frac{5 \pi}{6}\right)$
Therefore, 2x = $n \pi+x+\frac{5 \pi}{6}$, where n $\in$ Z
or x = $n \pi+x+\frac{5 \pi}{6}$, where n $\in$ Z.

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