Question

Evaluate each of the following :
$\frac{sin{30}^{\circ }-sin{90}^{\circ }+2cos{0}^{\circ }}{tan{30}^{\circ }tan{60}^{\circ }}$

Answer 1

We know that,

$\sin 30=\frac{1}{2}$

$\cos 0=1$

$\sin 90=1$

$\tan 30=\frac{1}{\sqrt{3}}$

$\tan 30=\sqrt{3}$

$\therefore \frac{\sin 30-\sin 90+2cos0}{\tan 30\tan 60}=\frac{\frac{1}{2}-1+2}{\frac{1}{\sqrt{3}}\times \sqrt{3}}$

$=\frac{3}{2}$