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  4. (1/ sin 10°)-(√3/ cos 10°)=

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Q. $\frac{1}{\sin 10^{\circ}}-\frac{\sqrt{3}}{\cos 10^{\circ}}=$

Trigonometric Functions

Solution:

$\frac{1}{\sin 10^{\circ}}-\frac{\sqrt{3}}{\cos 10^{\circ}}=\frac{\left[\cos 10^{\circ}-\sqrt{3} \sin 10^{\circ}\right]}{\sin 10^{\circ} \cos 10^{\circ}}$
$=\frac{2\left[\frac{1}{2} \cos 10^{\circ}-\frac{\sqrt{3}}{2} \sin 10^{\circ}\right]}{\sin 10^{\circ} \cos 10^{\circ}}$
$=\frac{2\left[\sin 30^{\circ} \cos 10^{\circ}-\cos 30^{\circ} \sin 10^{\circ}\right]}{\sin 10^{\circ} \cos 10^{\circ}}$
$=\frac{2\left[\sin \left(30^{\circ}-10^{\circ}\right)\right]}{\sin 10^{\circ} \cos 10^{\circ}}=\frac{2 \cdot 2 \sin \left(30^{\circ}-10^{\circ}\right)}{2 \sin 10^{\circ} \cos 10^{\circ}}=4 .$