What is the general solution for 4sin^2(x)=2 ?

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

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4sin^2(x)=2

4 sin^{2} (x) = 2

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

4 sin^{2} (x) = 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

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

cos (4 θ) = 0

t, L {sin (2 t)} = \frac{2}{s ^{2} + 4}

2 sec^{2} (x) + tan (x) = 5

1 - sin (x) = cos (2 x)

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