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Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSTrigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]2 Marks
Question
Prove that: $\sin 60^\circ = 2 \sin 30^\circ \cos 30^\circ $
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Answer

$\text{LHS} = \sin 60^\circ = \frac{\sqrt{3}}{2}$
$\text{RHS} = 2 \sin 60^\circ \cos 60^\circ =2 \times \frac{\sqrt{3}}{2} \times \frac{1}{2}=\frac{\sqrt{3}}{2}$
$\text{LHS} = \text{RHS}$

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