If ^ -1 2 x+ ^ -1 3 x= 4 , then x= - Vidyadip

MCQ

If $\tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4}$, then $x=$

A
-1
B
$\frac{1}{3}$
✓
$\frac{1}{6}$
D
$\frac{1}{2}$

✓

Answer

Correct option: C.

$\frac{1}{6}$

(c) : We have $\tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4}$
$
\begin{aligned}
& \Rightarrow \tan ^{-1}\left(\frac{2 x+3 x}{1-2 x \times 3 x}\right)=\frac{\pi}{4} ; x>0 \Rightarrow \frac{5 x}{1-6 x^2}=1 \\
& \Rightarrow 6 x^2+5 x-1=0 \Rightarrow(6 x-1)(x+1)=0 \Rightarrow x=\frac{1}{6}(\because x \neq-1)
\end{aligned}
$

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