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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 22

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 22

Answers (1)

Answer:

                1

Hint:

You must know the rules of inverse trigonometric function.

Given:

                3\tan^{-1}x+\cot^{-1}x=\pi

Solution:

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

\begin{aligned} &\Rightarrow \quad 3 \tan ^{-1} x+\left(\frac{\pi}{2}-\tan ^{-1} x\right)= \pi\\\\ &\Rightarrow \quad 3 \tan ^{-1} x-\tan ^{-1} x=\pi-\frac{\pi}{2} \\\\ &\Rightarrow \quad 2 \tan ^{-1} x=\frac{2 \pi-\pi}{2} \\\\ &\Rightarrow \quad 2 \tan ^{-1} x=\frac{\pi}{2} \\\\ &\Rightarrow \quad \tan ^{-1} x=\frac{\pi}{4} \\\\ &\Rightarrow \quad x=\tan \left(\frac{\pi}{4}\right) \end{aligned}        

\Rightarrow x=1        

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