Question

how to simplify the problem
please fastly​

Answer 1

$\large\rm{ \dfrac{1}{\sin 10^\circ} - \dfrac{\sqrt{3}}{\cos 10^\circ}}$

$\large\rm$

$\large\rm{ = 2 \Bigg [ \dfrac{1}{2 \ \sin 10°} - \dfrac{\sqrt{3}}{ 2 \ \cos 10^\circ} \Bigg ] }$

$\large\rm$

$\large\rm{ = 2 \Bigg [ \dfrac{\sin 30^\circ}{\sin 10^\circ} - \dfrac{\cos 30^\circ}{\cos 10^\circ} \Bigg ] }$

$\large\rm$

$\small\rm{ = 2 \Bigg [ \dfrac{ \sin 30^\circ \ \cos 10^\circ - \cos 30^\circ \ \sin10^\circ}{ \sin 10^\circ \ \cos 10^\circ} \Bigg ]}$

$\large\rm$

$\large\rm{ = 2 \Bigg [ \dfrac{ \sin 20^\circ}{ \sin 10^\circ \cos 10^\circ} \Bigg]}$

$\large\rm$

$\large\rm{ = 2 \times 2 \Bigg [\dfrac{ \sin 10^\circ \ \cos 10^\circ}{ \sin 10^\circ \cos 10^\circ} \Bigg ]}$

$\large\rm$

$\large\rm{ = 2 \times 2 \Bigg [ \dfrac{\cancel{\sin 10^\circ \ \cos 10^\circ}}{\cancel{\sin 10^\circ \cos 10^\circ}} \Bigg ]}$

$\large\rm$

$\large\rm{ = 4}$