What is the general solution for 6sin(x)-1=4sin(x) ?

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

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6sin(x)-1=4sin(x)

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

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

Solution steps

6 sin (x) - 1 = 4 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 (2 x) - sin (x) = 0, 0 \leq x < 2 π

3 sin^{2} (x) - cos^{2} (x) = 1

2 sin^{2} (θ) + 3 cos (θ) = 3

2 sin (θ) = 1

sin (2 x) (csc (2 x) - 2) = 0

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