Question

The value of the expression $\frac{1}{2} ( \sqrt{3} \sin 75^{\circ} - \cos \, 75^{\circ} )$ is :

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

Answer 1

Answer: (C)

Consider $\frac{1}{2} \left(\sqrt{3} \sin75^{\circ} - \cos75^{\circ}\right)$
$ = \frac{\sqrt{3}}{2} . \sin 75^{\circ} - \frac{1}{2} \cos75^{\circ} $
$= \sin60^{\circ}. \sin75^{\circ} - \cos60^{\circ}. \cos75^{\circ} $
$= - \left[\cos\left(75^{\circ}+ 60^{\circ}\right)\right] $
$= - \cos135 ^{\circ}$
$ = - \cos\left(180^{\circ} - 45^{\circ}\right) $
$= + \frac{1}{\sqrt{2}}$