Question

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

• A. $4$
• B. $6$
• C. $-2$
• D. $0$

Answer 1

Answer: (B)

$6$

We have,

$x\sin \frac{\pi }{6}{\cos }^2\frac{\pi }{4}=\frac{{\cot }^2\frac{\pi }{6}\sec \frac{\pi }{3}\tan \frac{\pi }{4}}{cose{c}^2\frac{\pi }{4}cosec\frac{\pi }{6}}$

Simplifying the equation we get,

$x\left(\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}{}^2}\right)=\frac{\left(\sqrt{3}{}^2\right)\left(2\right)\left(1\right)}{\left(\sqrt{2}{}^2\right)\left(2\right)}$

$\frac{x}{4}=\frac{3}{2}$

Therefore $x=6$

Hence answer is B