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  • Let <img alt="{\tan ^{ - 1}}\left( {\tan \frac{{5\pi }}{4}} \right) = \;\alpha ,\;{\tan ^{ - 1}}\

Let {\tan ^{ - 1}}\left( {\tan \frac{{5\pi }}{4}} \right) = \;\alpha ,\;{\tan ^{ - 1}}\;\left( { - \tan \frac{{2\pi }}{3}} \right)=\beta . Then

Option: 1

\alpha >\beta


Option: 2

4\alpha -3\beta \neq0


Option: 3

\alpha +\beta=\frac{7\pi}{12}


Option: 4

none of these


Answers (1)

best_answer

As we learnt

 

Important Results of Inverse Trigonometric Functions -

 

\tan ^{-1}\left ( \tan \Theta \right )= \Theta

- wherein

if \frac{-\pi }{2}< \Theta < \frac{\pi }{2}

 

 

 

{\tan ^{ - 1}}\;\left\{ {\tan \,\left( {\pi + \frac{\pi }{4}} \right)} \right\} = {\tan ^{ - 1}}\tan \frac{\pi }{4} = \frac{\pi }{4} = \alpha.

 {\tan ^{ - 1}}\;\left\{ { - \tan \,\left( {\pi - \frac{\pi }{3}} \right)} \right\} = {\tan ^{ - 1}}\tan \frac{\pi }{3} = \frac{\pi }{3} = \beta $.

Posted by

Divya Prakash Singh

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