Question

If $x\sin 45°{\cos }^{2}60°=\frac{({\tan }^{2}60°\cos ec30°)}{(sec45°co{t}^{2}30°)}$, then $x=$

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is C

$8$

Explanation for the correct option.

$\begin{array}{rcl}x\sin 45°{\cos }^{2}60°& =& \frac{({\tan }^{2}60°\cos ec30°)}{(sec45°co{t}^{2}30°)}\\ & \Rightarrow & x\left[\frac{1}{\sqrt{2}}\times {\left(\frac{1}{2}\right)}^2\right]=\frac{{\left(\sqrt{3}\right)}^2\times 2}{\sqrt{2}\times {\left(\sqrt{3}\right)}^2}\\ \Rightarrow x\left(\frac{1}{4\sqrt{2}}\right)& =& \frac{6}{3\sqrt{2}}\\ \Rightarrow x& =& \frac{6\times 4\sqrt{2}}{3\sqrt{2}}\\ \Rightarrow x& =& 8\end{array}$

Hence, option C is correct.