Question

If $3{\tan }^{-1}x+{\cot }^{-1}x=\pi$, then x equals :

• A. $0$
• B. $1$
• C. $-1$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$1$

$3{\tan }^{-1}x+{\cot }^{-1}x=\pi$

$2{\tan }^{-1}x+({\tan }^{-1}x+{\cot }^{-1}x)=\pi$

$2{\tan }^{-1}x+\frac{\pi }{2}=\pi$

$2{\tan }^{-1}x=\frac{\pi }{2}$

${\tan }^{-1}x=\frac{\pi }{4}$

$x=1$