What is the general solution for 5sin(x)=3sin(x)+sqrt(3) ?

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

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5sin(x)=3sin(x)+sqrt(3)

5 sin (x) = 3 sin (x) + 3

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Solution steps

5 sin (x) = 3 sin (x) + 3

Solve by substitution

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

sin (x) = \frac{3}{2} : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

9 cot^{2} (θ) - 16 = 0

cos (θ) = - \frac{3}{4}

sin^{2} (x) - 3 sin (x) + 2 = 0

sin (θ) = \frac{1}{5}

sin (4 x) = sin (2 x)

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