Question

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

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

Answer 1

Answer: (A)

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