Considering only the principal values of inverse functions, the set A= \xge0:tan^-1(2x)+tan^-1(3x)=fracpi4 \

Inverse Trigonometric Functions: Considering only the principal values of inverse functions, the set… | JEE Main 2019

JEE Main 2019 (Online) 12th January Morning ShiftQuestion 1

Considering only the principal values of inverse functions, the set $A=\left\{x\ge0:\tan^{-1}(2x)+\tan^{-1}(3x)=\frac\pi4\right\}$

Inverse Trigonometric Functions

Is an empty setContains more than two elementsContains two elementsIs a singleton✓ Correct answer

Solution

$\frac{5x}{1-6x^2}=1\Rightarrow6x^2+5x-1=0$, $x=\frac16$ or $x=-1$; only $x=\frac16\ge0$ works. $A$ is a singleton.