What is the general solution for 5sin(x)=2+sin(x) ?

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

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5sin(x)=2+sin(x)

5 sin (x) = 2 + sin (x)

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

Solution steps

5 sin (x) = 2 + 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

- 3 = 4 - 2 arctan (\frac{4 - 2 - C}{4 - C})

cos^{2} (x) + \frac{11}{2} cos (x) = 3 cos (x) - 1

23 sin (4 θ) = 3

3 tan (3 x) = 3

8 cos (3 x) = 2

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