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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 30

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 30

Answers (1)

Answer:

                -\frac{\pi}{3}

Hints:

You must know the rules and values of inverse trigonometric functions.

Given:

                \tan^{-1}\left ( \tan\frac{2\pi}{3}\right )

Solution:

                \tan^{-1}\left ( \tan\frac{2\pi}{3}\right )

We know, \tan^{-1}\tan x=x,x\: \epsilon \left ( -\frac{\pi}{2},\frac{\pi}{2}\right )

                \tan^{-1}\left ( \tan\frac{2\pi}{3} \right )=\tan^{-1}\left ( \tan\left ( \pi-\frac{\pi}{3} \right ) \right )                                        \left [ \tan\tan\left ( \pi-\theta \right ) =-\tan\theta \right ]

                \tan^{-1}\left ( \tan\left ( -\frac{\pi}{3} \right ) \right )   

                \Rightarrow -\frac{\pi}{3}

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