Question

The value of $\frac{\tan 330^{\circ }\sec 420^{\circ }\sin 300^{\circ }}{\tan 135^{\circ }\sin 210^{\circ }\sec 315^{\circ }}$ is equal to

• A. $\frac{1}{\sqrt{2}}$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

Answer: (B)

$\frac{\tan 330^{\circ }\sec 420^{\circ }\sin 300^{\circ }}{\tan 135^{\circ }\sin 210^{\circ }\sec 315^{\circ }}$
$=\frac{\tan {\left(360-30\right)}^{\circ }\sec {\left(360+60\right)}^{\circ }\sin {\left(360-60\right)}^{\circ }}{\tan {\left(180-45\right)}^{\circ }\sin {\left(180+30\right)}^{\circ }\sec {\left(360-45\right)}^{\circ }}$
$=\frac{-\tan 30^{\circ }\times \sec 60^{\circ }\times \sin 60^{\circ }}{\left(-\tan 45^{\circ }\right)\left(-\sin 30^{\circ }\right)\sec 45^{\circ }}$
$=\frac{1\times 2\times \sqrt{3}\times 2}{\sqrt{3}\times 2\times 1\times \sqrt{2}}\sqrt{2}$