Question

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

• A. $4$
• B. $6$
• C. $-2$
• D. $0$

Answer 1

Answer: (B)

$6$

$x\sin \frac{\pi }{6}{\cos }^2\frac{\pi }{4}=\frac{{\cot }^3\frac{\pi }{6}\sec \frac{\pi }{6}\tan \frac{\pi }{4}}{{\csc }^2\frac{\pi }{4}\csc \frac{\pi }{6}}$
$⟹x\times \frac{1}{2}\times \frac{1}{2}=\frac{(\sqrt{3}{)}^3\times \frac{2}{\sqrt{3}}\times 1}{(\sqrt{2}{)}^2\times 2}$
$⟹x\times \frac{1}{4}=\frac{3\sqrt{3}\times \frac{2}{\sqrt{3}}\times 1}{2\times 2}=\frac{3}{2}=\frac{1}{2}$
$⟹x=6$