What is the general solution for 2sin(3x)=2 ?

The general solution for 2sin(3x)=2 is x= pi/6+(2pin)/3

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2sin(3x)=2

2 sin (3 x) = 2

x = \frac{π}{6} + \frac{2 πn}{3}

Solution steps

2 sin (3 x) = 2

Divide both sides by

2

sin (3 x) = 1

General solutions for

sin (3 x) = 1

3 x = \frac{π}{2} + 2 πn

Solve

3 x = \frac{π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

sin (x) = \frac{2}{3}

2 (- cos^{2} (x) - sin (x) + sin^{2} (x)) = 0

cos (x) - sin (x) = \frac{2}{3}

0 = ((10 cos (x)) - 8)^{2} ((10 sin (x)) - 6)^{2}

tan (x) = \frac{4}{2}

What is the general solution for 2sin(3x)=2 ?
The general solution for 2sin(3x)=2 is x= pi/6+(2pin)/3