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Trigonometric Ratios — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Ratios2 Marks
Question
If A, B, C are the interior angles of a $\triangle\text{ABC},$ show that:
$\cos\frac{\text{B+C}}{2}=\sin\frac{\text{A}}{2}$
✓

Answer

$\cos\frac{\text{B+C}}{2}=\sin\frac{\text{A}}{2}$
$=\text{L.H.S}$
$=\cos\frac{\text{B+C}}{2}$
$=\cos\frac{180^\circ-\text{A}}{2}$
$=\cos\Big(90^\circ-\frac{\text{A}}{2}\Big)$
$=\sin\frac{\text{A}}{2}$
$=\text{R.H.S}$

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