Question

Find the value of $\sqrt{\frac{1-{\sin }^2{30}^0}{1-{\cos }^2{30}^0}}$

Answer 1

We know that,

${\sin }^2\theta +{\cos }^2\theta =1$

$\Rightarrow {\sin }^2\theta =1-{\cos }^2\theta$ ---(1)

${\cos }^2\theta =1-{\sin }^2\theta$ ---(2)

Now,

$\sqrt{\frac{1-{\sin }^2{30}^0}{1-{\cos }^2{30}^0}}$

$=\sqrt{\frac{{\cos }^2{30}^{\circ }}{{\sin }^2{30}^{\circ }}}$ [Since, from (1) and (2)]

$=\sqrt{{\cot }^2{30}^{\circ }}$

$=\cot {30}^{\circ }$

$=\sqrt{3}$

$\therefore \sqrt{\frac{1-{\sin }^2{30}^0}{1-{\cos }^2{30}^0}}=\sqrt{3}$.