What is the general solution for 7sin^2(x)=sin(x) ?

The general solution for 7sin^2(x)=sin(x) is x=0.14334…+2pin,x=pi-0.14334…+2pin,x=2pin,x=pi+2pin

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7sin^2(x)=sin(x)

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

x = 0.14334 \dots + 2 πn, x = π - 0.14334 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{1}{7}, sin (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{7}) + 2 πn, x = π - arcsin (\frac{1}{7}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.14334 \dots + 2 πn, x = π - 0.14334 \dots + 2 πn, x = 2 πn, x = π + 2 πn

sin (2 θ) + cos (2 θ) = 1

tan (4 x) = 3, 0 \leq x \leq 2 π

6 arctan (x) = 2 π

2 cos^{2} (x) - sin (x) + 1 = 0

7 csc (x) - 3 = 11

What is the general solution for 7sin^2(x)=sin(x) ?
The general solution for 7sin^2(x)=sin(x) is x=0.14334…+2pin,x=pi-0.14334…+2pin,x=2pin,x=pi+2pin