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)

$7$

Answer 2

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