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  • explain solution rd sharma class 12 chapter inverse trigonometric functions exercise 3 point 2 question 4 sub question (iv) maths

explain solution rd sharma class 12 chapter inverse trigonometric functions exercise 3.2 question 4  sub question (iv) maths

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Answer: \pi

Hint: The range of the principal value branch of  \cos ^{-1} is \left [ 0,\pi \right ]

Given:    \cos ^{-1}\left ( \tan \frac{3\pi }{4} \right )

Solution:

  \cos ^{-1}\left ( \tan \frac{3\pi }{4} \right ) = \cos ^{-1}\left ( \tan \left ( \frac{\pi }{2}+\frac{3\pi }{4} \right ) \right )

                                   =cos ^{-1}(-1)

\therefore \cos ^{-1}\left ( \tan \frac{3\pi }{4} \right )=\pi

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