Question

Simplify $\sqrt{\frac{1-{\sin }^2\theta }{1-{\cos }^2\theta }}$.

Answer 1

Now,

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

$=\sqrt{\frac{{\cos }^2\theta }{{\sin }^2\theta }}$ [ Since ${\sin }^2\theta +{\cos }^2\theta =1$]

$=\sqrt{{\cot }^2\theta }$

$=|cot\theta |$.