Question

Value of $\cot [\frac{\pi }{4}-2{\cot }^{-1}3]$

• A. 3
• B. 7
• C. 9
• D. $\frac{3}{4}$

Answer 1

The correct option is B 7

Given,

$\cot [\frac{\pi }{4}-2{\cot }^{-1}3]$

Let, ${\cot }^{-1}3=A$

$=\cot [\frac{\pi }{4}-2A]$

$=\frac{1}{\tan [\frac{\pi }{4}-2A]}$

$=\frac{1+\tan 2A}{1-\tan 2A}$

Now,

$\cot A=3$

$\tan A=\frac{1}{3}$

$\tan 2A=\frac{2\tan A}{1-{\tan }^{2}A}$

$=\frac{2\times \frac{1}{3}}{1-{\left(\frac{1}{3}\right)}^2}$

$=\frac{3}{4}$

$\cot [\frac{\pi }{4}-2{\cot }^{-1}3]=\frac{1+\frac{3}{4}}{1-\frac{3}{4}}=7$