Question

Solve for $x:{\left\{xcos\left(co{t}^{-1}x\right)+sin\left(co{t}^{-1}x\right)\right\}}^2=\frac{51}{50}$,

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{5\sqrt{2}}$
• C. $2\sqrt{2}$
• D. $5\sqrt{2}$

Answer 1

Answer: (B)

${\left\{xcos\left(co{t}^{-1}x\right)+sin\left(co{t}^{-1}x\right)\right\}}^2=\frac{51}{50}$
$\Rightarrow {\left\{xcos\left(ta{n}^{-1}\frac{1}{x}\right)+sin\left(ta{n}^{-1}\frac{1}{x}\right)\right\}}^2=\frac{51}{50}$
$\Rightarrow {\left(\frac{x^2}{\sqrt{1+x^2}}+\frac{1}{\sqrt{1+x^2}}\right)}^2=\frac{51}{50}$
$\Rightarrow \frac{\left(x^2+1\right)}{\left(x^2+1\right)}=\frac{51}{50}$
$\Rightarrow x^2+1=\frac{51}{50}$
$\Rightarrow x=\pm \frac{1}{5\sqrt{2}}$