Question

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

• A. $4$
• B. $6$
• C. $-2$
• D. $0$

Answer 1

The correct option is B $6$

$x\sin \frac{\pi }{6}{\cos }^2\frac{\pi }{4}=\frac{{\cot }^2\frac{\pi }{6}\sec \frac{\pi }{3}\tan \frac{\pi }{4}}{co{\sec }^2\frac{\pi }{4}co\sec \frac{\pi }{6}}$
$\Rightarrow x\left(\frac{1}{2}\right){\left(\frac{1}{\sqrt{2}}\right)}^2=\frac{{\left(\sqrt{3}\right)}^2\times 2\times 1}{{\left(\sqrt{2}\right)}^{2}2}$
$\Rightarrow$ $x=3\times 2$ $\Rightarrow$ $x=6$