Question

$cot\left(\frac{\pi }{4}-2co{t}^{-1}3\right)=$

• A. $7$
• B. $6$
• C. $5$
• D. None of these

Answer 1

Answer: (A)

$cot\left(\frac{\pi }{4}-2co{t}^{-1}3\right)$
$=cot\left(\frac{\pi }{4}-2ta{n}^{-1}\frac{1}{3}\right)$
$=cot\left\{\frac{\pi }{4}-ta{n}^{-1}\left(\frac{\frac{2}{3}}{1-\frac{1}{9}}\right)\right\}$
$=cot\left\{\frac{\pi }{4}-ta{n}^{-1}\left(\frac{3}{4}\right)\right\}$
$=\frac{1}{tan\left\{\frac{\pi }{4}-ta{n}^{-1}\left(\frac{3}{4}\right)\right\}}=\frac{1+\frac{3}{4}}{1-\frac{3}{4}}=7$