Question

Solution of the equation $co{t}^{-1}x+si{n}^{-1}\frac{1}{\sqrt{5}}=\frac{\pi }{4}$

• A. x = 3
• B. x=1/√5
• C. x = 0
• D. x=-3

Answer 1

The correct option is A

x = 3

We have, $co{t}^{-1}x+si{n}^{-1}\frac{1}{\sqrt{5}}=\frac{\pi }{4}$
$\Rightarrow ta{n}^{-1}\frac{1}{x}+ta{n}^{-1}\frac{1/\sqrt{5}}{\sqrt{1-\frac{1}{5}}}=\frac{\pi }{4}$
$\Rightarrow ta{n}^{-1}\frac{1}{x}+ta{n}^{-1}\frac{1}{2}=ta{n}^{-1}1$
$\Rightarrow ta{n}^{-1}\frac{1}{x}=ta{n}^{-1}1-ta{n}^{-1}\frac{1}{2}$
$\Rightarrow ta{n}^{-1}\frac{1}{x}=ta{n}^{-1}\left(\frac{1-\frac{1}{2}}{1+1.\frac{1}{2}}\right)$
$\Rightarrow ta{n}^{-1}\frac{1}{x}=ta{n}^{-1}(\frac{1}{3}\Rightarrow x=3)$