Inverse Trigonometric Functions Question 91
Question: If $ {{\tan }^{-1}}(2x)+ta{n^{-1}}(3x)=\frac{\pi }{4} $ then x is equal to
Options:
A) $\frac{1}{6}$
B) -2
C) 1
D) 2
Show Answer
Answer:
Correct Answer: A
Given: $ {{\tan }^{-1}}(2x)+ta{n^{-1}}(3x)=\frac{\pi }{4} $
$ \Rightarrow {{\tan }^{-1}}\frac{(2x+3x)}{(1-2x.3x)}={{\tan }^{-1}}(1) $
$ \Rightarrow \frac{5x}{1-6x^{2}}=1\Rightarrow 6x^{2}+5x-1=0 $
$ \Rightarrow (6x-1)(x+1)=0\Rightarrow x=\frac{1}{6}or-1. $
BETA
