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The value of cos-1 \left( { - \frac{1}{2}} \right) - 2{\sin ^{ - 1}}\left( {\frac{1}{2}} \right) + 3{\cos ^{ - 1}}\left( { - \frac{1}{{\sqrt 2 }}} \right) - 4{\tan ^{ - 1}}( - 1) is equal to

Option: 1

\frac{{7\pi }}{4}


Option: 2

\frac{{11\pi }}{4}


Option: 3

\frac{{\pi }}{12}


Option: 4

\frac{{25\pi }}{12}


Answers (1)

best_answer

As we learnt

Important Results of Inverse Trigonometric Functions -

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

-

We have {\cos ^{ - 1}}\left( { - \frac{1}{2}} \right) - 2{\sin ^{ - 1}}\frac{1}{2} + 3{\cos ^{ - 1}}\left( { - \frac{1}{{\sqrt 2 }}} \right) - 4{\tan ^{ - 1}}( - 1)

                      = \frac{{2\pi }}{3} - 2 \times \frac{\pi }{6} + 3 \times \frac{{3\pi }}{4} - 4\;\left( {\frac{{ - \pi }}{4}} \right) = \frac{{25\pi }}{{12}}

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Nehul

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