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

The general solution for 1/2 =sin^2(x) is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin

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1/2 =sin^2(x)

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

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

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

Switch sides

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

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

sin (x) = - \frac{1}{2} : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

- 12 sin^{2} (θ) + 3 = 0

2 cot^{2} (x) - 4 = 2

4 sin^{2} (θ) - 3 = 0, 0 \leq θ \leq 2 π

4 sin (B) + 8 = 0

4 cos (x) - 5 = - 7

What is the general solution for 1/2 =sin^2(x) ?
The general solution for 1/2 =sin^2(x) is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin