Question

Let the function $f(x)=\frac{\mathrm{arccot}\frac{x}{2}+\mathrm{arccot}\frac{x}{3}}{\arctan \frac{x}{2}+\arctan \frac{x}{3}}$, then $f(1)$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

We have, $f(1)=\frac{{\cot }^{-1}\frac{1}{2}+{\cot }^{-1}\frac{1}{3}}{{\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{1}{3}}=\frac{{\tan }^{-1}2+{\tan }^{-1}3}{{\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{1}{3}}=\frac{\frac{3\pi }{4}}{\frac{\pi }{4}}=3$