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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 19

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 19

Answers (1)

Answer:

                \pm \frac{\pi}{6}

Hint:

You must know the rules of inverse trigonometric function.

Given:

                \tan^{-1}\left ( \cot\theta \right )=2\theta

Solution:

                \tan^{-1}\left ( \cot\theta \right )=2\theta

\Rightarrow \cot\theta=\tan2\theta        

\Rightarrow \frac{1}{\tan\theta}=\frac{2\tan \theta}{1-\tan^{2}\theta}        

\Rightarrow 2\tan^{2}\theta=1-\tan^{2}\theta        

\Rightarrow 3\tan^{2}\theta=1        

\Rightarrow \tan^{2}\theta=\frac{1}{3}        

\Rightarrow \tan\theta=\pm \frac{1}{\sqrt{3}}        

\Rightarrow \theta=\pm \frac{\pi}{6}        

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