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Value of \tan^{-1} (\tan \frac{4\pi}{3}) is

Option: 1

\frac{4\pi}{3}


Option: 2

\frac{\pi}{3}


Option: 3

Both option 1 and option 2


Option: 4

None of these


Answers (1)

best_answer

\\\tan^{-1} (\tan \frac{4\pi}{3})\neq \frac{4\pi}{3}\ \,\,as \,\,\frac{4\pi}{3} \text{ is not in the range of } (-\frac{\pi}{2},\frac{\pi}{2})\\\\ \text{We can write it as } \tan^{-1} (\tan (\pi+ \frac{\pi}{3}))= \tan^{-1} (\tan (\frac{\pi}{3}))= \frac{\pi}{3} \\(\,\,as \,\,\frac{\pi}{3} \text{ lies in } (-\frac{\pi}{2},\frac{\pi}{2}))

Posted by

Sanket Gandhi

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