What is the general solution for 2sin^2(x)=1+sin(x) ?

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

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2sin^2(x)=1+sin(x)

2 sin^{2} (x) = 1 + sin (x)

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

Solution steps

2 sin^{2} (x) = 1 + sin (x)

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

6 sec^{2} (x) - 6 = 0

- 2 cos (x) + cos^{2} (x) + 4 = 3

- 2 sin (b) - 6 = sin (b) - 3

cos (t) = - sin (t)

cos (4 x) \cdot 4 = 0

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