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Question Bank - P2 — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuestion Bank - P21 Mark
Question
Prove that $\ce{cosec} \ \theta  \sqrt{1-\cos ^2 \theta}=1$
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Answer

$\text { L.H.S }=\operatorname{cosec} \theta \times \sqrt{1-\cos ^2 \theta}$
$=\operatorname{cosec} \theta \times \sqrt{\sin ^2 \theta}   \ldots\left[\begin{array}{l}\because \sin ^2 \theta+\cos ^2 \theta=1 \\ \therefore 1-\cos ^2 \theta=\sin ^2 \theta\end{array}\right]$
$=\operatorname{cosec} \theta \times \sin \theta$
$=1 \ldots \ldots[\because \sin \theta \times \operatorname{cosec} \theta=1]$
$=\text { R.H.S }$

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