Browse Questions

# The value of the expression $(\sqrt 3\sin 75^{\large\circ}-\cos 75^{\large\circ})$ is

$\begin{array}{1 1}(a)\;2\sin 15^{\large\circ}&(b)\;1+\sqrt 3\\(c)\;2\sin 105^{\large\circ}&(d)\;\sqrt 2\end{array}$

The given expression
$\sqrt 3\sin 75^{\circ}-\cos 75^{\large\circ}$
$\Rightarrow 2(\large\frac{\sqrt 3}{2}$$\sin 75^{\circ}-\large\frac{1}{2}$$\cos 75^{\large\circ})$
$\Rightarrow 2(\cos 30^{\large\circ}-\sin 75^{\large\circ}-\sin 30^{\large\circ}\cos 75^{\large\circ})$
$\Rightarrow 2\sin(75^{\large\circ}-30^{\large\circ})$
$\Rightarrow 2\sin 45^{\large\circ}$
$\Rightarrow 2\times \large\frac{1}{\sqrt 2}$
$\Rightarrow \sqrt 2$
Hence (d) is the correct option.