Question

If x sin 45° cos² 60° = $\frac{{\tan }^{2}60°\mathrm{cosec}30°}{\sec 45°{\cot }^{2°}30°}$, then x =
(a) 2
(b) 4
(c) 8
(d) 16

Answer 1

(c) 8

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ x\sin 45°{\cos }^{2}60°=\frac{{\tan }^{2}60°\cos ec30°}{\sec 45°{\cot }^{2}30°} \\ \Rightarrow x\times \left(\frac{1}{\sqrt{2}}\right)\times {\left(\frac{1}{2}\right)}^2=\frac{{\left(\sqrt{3}\right)}^2\times \left(2\right)}{\left(\sqrt{2}\right)\times {\left(\sqrt{3}\right)}^2} \\ \Rightarrow \frac{x}{4\sqrt{2}}=\frac{6}{3\sqrt{2}} \\ \Rightarrow x=\frac{6}{3\sqrt{2}}\times 4\sqrt{2} \\ \Rightarrow x=8 \end{gathered}$$