What is the general solution for 5sin^2(x)=sin(x) ?

The general solution for 5sin^2(x)=sin(x) is x=0.20135…+2pin,x=pi-0.20135…+2pin,x=2pin,x=pi+2pin

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5sin^2(x)=sin(x)

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

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{1}{5}, sin (x) = 0

sin (x) = \frac{1}{5} : x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn, x = 2 πn, x = π + 2 πn

- sin (2 x) \cdot 2 = 0

sin (x) = 3 cos (x)

cos (2 t) = cos (t)

cos (x) + cos (2 x) + cos (3 x) = 0

2 cot (θ) - 7 = 0

What is the general solution for 5sin^2(x)=sin(x) ?
The general solution for 5sin^2(x)=sin(x) is x=0.20135…+2pin,x=pi-0.20135…+2pin,x=2pin,x=pi+2pin