Solve tan 2 x=-cot left(x+frac{π}{3}right)

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Trigonometrical Equations

easy

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

Option A

Option B

Option C

Option D

Solution

We have, $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$

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

or $\tan 2 x=\tan \left(x+\frac{5 \pi}{6}\right)$

Therefore $2 x=n \pi+x+\frac{5 \pi}{6},$ where $n \in Z$

or $x=n \pi+\frac{5 \pi}{6},$ where $n \in Z$

Standard 11

Mathematics

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