Question

$\sqrt{\frac{1-si{n}^2{60}^{\circ }}{1-co{s}^2{60}^{\circ }}}$ is $\frac{1}{\sqrt{m}}$, find the value of m.

Answer 1

$\sqrt{\frac{1-{\sin }^2{60}^0}{1-{\cos }^2{60}^0}}$

= $\sqrt{\frac{{\cos }^2{60}^{\circ }}{{\sin }^2{60}^{\circ }}}$

= $\frac{\cos {60}^{\circ }}{\sin {60}^{\circ }}$

= $\cot {60}^{\circ }$

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