What is the general solution for 3sin^2(x)=sin(x) ?

The general solution for 3sin^2(x)=sin(x) is x=0.33983…+2pin,x=pi-0.33983…+2pin,x=2pin,x=pi+2pin

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3sin^2(x)=sin(x)

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

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{1}{3}, sin (x) = 0

sin (x) = \frac{1}{3} : x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = 2 πn, x = π + 2 πn

2 cos (2 θ) - 3 cos (θ) + 12 = 5 cos (θ) + 7

sin (4 x) - sin (x) = 0

tan (θ) = \frac{7}{5}

sin (t) = \frac{2}{5}

tan (x) - 1 = sec (x)

What is the general solution for 3sin^2(x)=sin(x) ?
The general solution for 3sin^2(x)=sin(x) is x=0.33983…+2pin,x=pi-0.33983…+2pin,x=2pin,x=pi+2pin