Question

Prove that $cosec\theta \sqrt{1-{\cos }^2\theta }=1$.

Answer 1

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

LHS = $cosec\theta \sqrt{(1-co{s}^2\theta )}$

$=cosec\theta \sqrt{{\sin }^2\theta }$

$=cosec\theta \sin \theta$

$=\frac{1}{sin\theta }\times sin\theta$

$=1$

$=RHS$