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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Exercise Multiple Choice Questions Question 18 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Exercise Multiple Choice Questions Question 18 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{5}

Hint: \tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}

Given: \tan ^{-1} 3+\tan ^{-1} x=\tan ^{-1} 8

We have to compute x.

Solution:

We know that,

\begin{aligned} &\tan ^{-1} 3+\tan ^{-1} x=\tan ^{-1} 8 \\ &\tan ^{-1}\left(\frac{3+x}{1-3 x}\right)=\tan ^{-1} 8 \end{aligned}

\left(\frac{3+x}{1-3 x}\right)=8

\begin{aligned} &3+x=8-24 x \\ &3-8=-24 \mathrm{x}-\mathrm{x} \\ &25 x=5 \\ &\mathrm{x}=\frac{1}{5} \end{aligned}

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