Question

Find the value of x from the equation $x\sin \frac{\pi }{6}{\cos }^2\frac{\pi }{4}=\frac{{\cot }^2\frac{\pi }{6}\sec \frac{\pi }{3}\tan \frac{\pi }{4}}{\cos {\sec }^2\frac{\pi }{4}\cos \sec \frac{\pi }{6}}$

• A. 4
• B. 6
• C. -2
• D. 0

Answer 1

The correct option is B 6

$x\sin \frac{\pi }{6}{\cos }^2\frac{\pi }{4}=\frac{{\cot }^2\frac{\pi }{6}\sec \frac{\pi }{3}\tan \frac{\pi }{4}}{\cos {\sec }^2\frac{\pi }{4}\cos \sec \frac{\pi }{6}}$
$\Rightarrow x\times \frac{1}{2}(\frac{1}{\sqrt{2}}{)}^2=\frac{(\sqrt{3}{)}^2.2.1}{(\sqrt{2}{)}^2.2}$
$\Rightarrow x\times \frac{1}{4}=\frac{\mathrm{3.2.1}}{2.2}$
$\Rightarrow x\times \frac{1}{4}=\frac{3}{2}$
$\Rightarrow x=6$
Option B is correct.