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

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

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

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

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

Solution steps

2 + sin (x) = 5 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 cos (θ) + 5 = 0

sin (x) cos (x) = cos (x)

2 cos (2 θ) + 1 = 0, 0 \leq θ \leq 2 π

cot (x) sin (x) + cot (x) = 0

4 cos (2 θ) = 4 sin (2 θ)

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