What is the general solution for 4sin(x)-1=2sin(x) ?

The general solution for 4sin(x)-1=2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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4sin(x)-1=2sin(x)

4 sin (x) - 1 = 2 sin (x)

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

Solution steps

4 sin (x) - 1 = 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

sin (θ) cos (θ) = sin (θ)

7 cos (x) + 4 = - cos (x)

2 sin^{2} (θ) - sin (θ) - 1 = 0, 0 \leq θ < 2 π

3 sin (x) = tan (x)

cos^{2} (θ) + cos (θ) = sin^{2} (θ)

What is the general solution for 4sin(x)-1=2sin(x) ?
The general solution for 4sin(x)-1=2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin