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Trigonometric Identities — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Identities2 Marks
Question
Prove the following trigonometric identities.
$\frac{\cot\text{A}-\cos\text{A}}{\cot\text{A}+\cos\text{A}}=\frac{\text{cosec A}-1}{\text{cosec A}+1}$
✓

Answer

$\text{L.H.S}=\frac{\frac{\cos\text{A}}{\sin\text{A}}-\cos\text{A}}{\frac{\cos\text{A}}{\sin\text{A}}+\cos\text{A}}\ \Big[\because \cot\text{A}=\frac{\cos\text{A}}{\sin\text{A}}\Big]$
$=\frac{\cos\text{A}\Big[\frac{1}{\sin\text{A}}-1\Big]}{\cos\text{A}\Big[\frac{1}{\sin\text{A}}+1\Big]}$
$=\frac{\text{cosec A}-1}{\text{cosec A}+1}=\text{R.H.S}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$

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