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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 14

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 14

Answers (1)

Answer:

                \tan\frac{5\pi}{12}

Hint:

You must know the rules of inverse trigonometric function.

Given:

\tan^{-1}x-\cot^{-1}x=\tan^{-1}\sqrt{3}, then find \cot^{-1}x+\cot^{-1}y

Solution:

\tan^{-1}x-\cot^{-1}x=\tan^{-1}\sqrt{3}

\Rightarrow \tan^{-1}x-\left [ \frac{\pi}{2}-\tan^{-1}x \right ]=\frac{\pi}{3}         

\Rightarrow \tan^{-1}x-\frac{\pi}{2}+\tan^{-1}x=\frac{\pi}{3}        

\Rightarrow 2\tan^{-1}x=\frac{\pi}{3}+\frac{\pi}{2}        

\Rightarrow 2\tan^{-1}x=\frac{5\pi}{6}        

\Rightarrow \tan^{-1}x=\frac{5\pi}{12}        

\Rightarrow x=\tan\frac{5\pi}{12}        

Posted by

infoexpert27

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