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

The Correct Option is 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 \sec60^{\circ } \times \sin60^{\circ }}{\left(-\tan 45^{\circ }\right) \left(-\sin 30^{\circ }\right) \sec 45^{\circ } } $
$= \frac{1 \times 2\times \sqrt{3} \times 2}{\sqrt{3} \times 2\times 1\times \sqrt{2}}\sqrt{2}$