Question

cosec θ.${\displaystyle \sqrt{1-{\cos }^2\theta }=1}$ हे सिद्ध करा.

Answer 1

डावी बाजू = ${\displaystyle \text{cosec} \theta \times \sqrt{1-{\cos }^2\theta }}$

= ${\displaystyle \text{cosec} \theta \times \sqrt{{\sin }^2\theta }}$   ......${\displaystyle \left[\begin{array}{c}\because {\sin }^2\theta +{\cos }^2\theta =1\\ \therefore 1-{\cos }^2\theta ={\sin }^2\theta \end{array}\right]}$

= cosec θ × sin θ

= 1     ......[∵ sin θ × cosec θ = 1]

= उजवी बाजू