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Basic Trigonometric Identities

Solve the fol...

Question

Solve the following equations.
$s i n 2 x + s i n (π - 8 x) = \sqrt{2} c o s 3 x .$

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Solution

$sin 2 x + sin (π - 8 x) = \sqrt{2} cos 3 x$
$sin 2 x + sin 8 x = \sqrt{2} cos 3 x$
$2 sin \frac{(2 x + 8 x)}{2} cos \frac{(2 x - 8 x)}{2} = \sqrt{2} cos 3 x$
$2 sin 5 x cos 3 x = \sqrt{2} cos 3 x$
$sin 5 x = \frac{1}{\sqrt{2}}$
$sin 5 x = \frac{π}{4}, x = \frac{π}{20}$

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