Question

If $xsin\frac{\pi }{4}co{s}^2\frac{\pi }{3}=\frac{ta{n}^2\left(\pi /3\right)cosec\left(\pi /6\right)}{sec\left(\pi /4\right)co{t}^2\left(\pi /6\right)}$, then $x=$

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

Answer: (C)

$xsin45^{\circ }co{s}^{2}60^{\circ }=\frac{ta{n}^{2}60^{\circ }cosec30^{\circ }}{sec45^{\circ }co{t}^{2}30^{\circ }}$
$\Rightarrow x\cdot \frac{1}{\sqrt{2}}\cdot \frac{1}{4}=\frac{3\cdot 2}{\sqrt{2}\cdot 3}$
$\Rightarrow x=8$.