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Trigonometric Identities — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Identities2 Marks
Question
Prove the following trigonometric identities.
$(1+\cot^2\text{A})\sin^2\text{A}=1$
✓

Answer

$\text{L.H.S}=(1+\cot^2\text{A})\sin^2\text{A}$
$=\text{cosec}^2\text{A}\times\sin^2\text{A}\ [1+\cot^2\theta=\text{cosec}^2\theta]$
$=\frac{1}{\sin^2\text{A}}\times\sin^2\text{A}$
$=1=\text{R.H.S}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$

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