What is the general solution for 3sin(x)-2=5sin(x)-1 ?

The general solution for 3sin(x)-2=5sin(x)-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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3sin(x)-2=5sin(x)-1

3 sin (x) - 2 = 5 sin (x) - 1

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

3 sin (x) - 2 = 5 sin (x) - 1

Solve by substitution

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

1 + cos (θ) = 3 cos (θ)

sin (x) = - sin^{2} (x)

tan (x) = \frac{1}{3}

cos (θ) + 1 = 2 sin^{2} (θ)

4 sin (θ) + 3 = 0

What is the general solution for 3sin(x)-2=5sin(x)-1 ?
The general solution for 3sin(x)-2=5sin(x)-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin