Question

If $co{t}^{-1}\left(x\right)+{\tan }^{-1}\left(3\right)=\frac{\pi }{2}$, then $x=$

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $3$
• D. $4$

Answer 1

The correct option is C

$3$

Find the value of $x$:

Given, $co{t}^{-1}\left(x\right)+{\tan }^{-1}\left(3\right)=\frac{\pi }{2}$

As we know, $\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathit{c}\mathit{o}{\mathit{t}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{\pi }}{\mathbf{2}}$

$\mathbf{\therefore }\mathbf{}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}$

Alternatively,

$co{t}^{-1}\left(x\right)+{\tan }^{-1}\left(3\right)=\frac{\pi }{2}$

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

${\tan }^{-1}\left(3\right)={\tan }^{-1}\left(x\right)$

$\mathbf{\therefore }\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}$

Hence, Option ‘C’ is Correct.