Question

Find the principal value of tan inverse of (-1) ​

Answer 1

Answer:

Solution: If the principal value of tan−1 x is θ then we know, - π2 < θ < π2. Therefore, theprincipal value of tan−1(1/√3) is π6.

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Answer 2

Step-by-step explanation:

$\tt Principal\:value\:of\:{tan}^{-1}(-1) \\ \\ \tt Let\: {tan}^{-1}(-1) = \theta \\ \\ \tt tan \theta = -1 \\ \\ \tt Principal\:value\:of\:{tan}^{-1}(-1) \:lies \:between \: (-\frac{\pi}{2} , \frac{\pi}{2}) \\ \\ \tt tan \theta = tan (-\frac{\pi}{4}) \\ \\ \tt \theta = -\frac{\pi}{4} \\ \\ \tt \boxed{\bold{\underline{\red{\tt So\:the\:principal\:value\:of\:{tan}^{-1}(-1) \: is \: - \frac{\pi}{4}}}}}$