What is the general solution for 8sin^2(x)-2=0 ?

The general solution for 8sin^2(x)-2=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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8sin^2(x)-2=0

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

y, sin (x) = x (1 + tan (y))

sin (2 x) - sin (x) = 0, (0, 2 π)

sin^{4} (x) + cos^{4} (x) = \frac{7}{9}

tan (\frac{θ}{5}) + 3 = 0

3 tan (x) - 3 = 0, 0 \leq x < 2 π

What is the general solution for 8sin^2(x)-2=0 ?
The general solution for 8sin^2(x)-2=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin