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Trigonometric Identities — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities2 Marks
Question
Prove the following identities:
$\cot^2\theta-\frac{1}{\sin^2\theta}=-1$
✓

Answer

$\text{L.H.S.}=\cot^2\theta-\frac{1}{\sin^2\theta}$
$=\cot^2\theta-\text{cosec}^2\theta$
$=-1$ $\big(\text{since}1+\cot^2\theta=\text{cosec}^2\theta=-1\big)$
$=\text{R.H.S.}$

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