Question

$if \: \sin(2x) = \frac{ \sqrt{3} }{2} then \: find \: the \: value \: of \: \sin(3x)$

Answer 1

$since \: \sin(2x) = \frac{ \sqrt{3} }{2} \\ \\ but \: \sin(60) = \frac{ \sqrt{3} }{2} \\ \\ therefore \: \: \sin(2x) = \sin(60) \\ \\ or \: \: 2x = 60 \\ \\ or \: \: x = \frac{60}{2} = 30 \\ \\ therefore \: \: \sin(3x) = \sin(3 \times30) \\ \\ = \sin(90) = 1 \\ \\ \: hope \: it \: helps...$