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Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds2 Marks
Question
Prove that: $\sin^224^\circ-\sin^26^\circ=\frac{\sqrt{5}-1}{8}$
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Answer

$\text{LHS}=\sin^224^\circ-\sin^26^\circ$ $=\sin(24+6)\sin(24-6)\\ [\because\sin(\text{A+B})\sin(\text{A}-\text{B}=\sin^2\text{A}-\sin^2\text{B})]$ $=\sin30^\circ\sin18^\circ$ $=\frac{1}{2}.\frac{\sqrt{5}-1}{4}\Big[\because\sin18^\circ=\frac{\sqrt{5}-1}{4}\Big]$ $=\frac{\sqrt{5}-1}{8}$ $=\text{RHS}$

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