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Solving Simultaneous Trigonometric Equations

Prove the fol...

Question

Prove the following identity:
$sin α + 2 sin 3 α + sin 5 α = 4 sin 3 α {cos}^{2} α$

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Solution

$sin α + 2 sin 3 α + sin 5 α$
$= 2 sin 3 α cos 2 α + 2 sin 3 α$
$= 2 sin 3 α (cos 2 α + 1)$
$= 2 sin 3 α \times 2 {cos}^{2} α$
$= {4 cos}^{2} α sin 3 α$

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