What is the general solution for 3sin(x)=1+sin(x) ?

The general solution for 3sin(x)=1+sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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3sin(x)=1+sin(x)

3 sin (x) = 1 + sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

3 sin (x) = 1 + sin (x)

Solve by substitution

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 sin (x - \frac{π}{6}) + 1 = 0

3 - 3 sin (θ) = 6 cos^{2} (θ)

sin (x) + sin^{2} (x) + cos^{2} (x) = 1

tan (3 x) = 5 tan (x)

2 cos (2 x) - 2 = 0

What is the general solution for 3sin(x)=1+sin(x) ?
The general solution for 3sin(x)=1+sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin