What is the general solution for 2*sin^2(x)-1=0 ?

The general solution for 2*sin^2(x)-1=0 is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin

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2*sin^2(x)-1=0

2 \cdot sin^{2} (x) - 1 = 0

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

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

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

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

tan (θ) = \frac{220}{370}

2 tan (2 x) = - 42

(4 sin (x) + 1) (2 sin (x) + 1) = 0

2 sin (3 x) \cdot sin (x) = 1

What is the general solution for 2*sin^2(x)-1=0 ?
The general solution for 2*sin^2(x)-1=0 is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin