What is the general solution for 8sin^2(x)-6=0 ?

The general solution for 8sin^2(x)-6=0 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin

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8sin^2(x)-6=0

8 sin^{2} (x) - 6 = 0

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

Solution steps

8 sin^{2} (x) - 6 = 0

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

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

sin (x) = - \frac{3}{2} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

2 cot^{2} (x) = 6

sin (x) = 0.3456

5 cos^{2} (x) + 3 cos (x) = 0, (0, 2 π)

cos (x) - 2 sin (2 x) = 0

x, cos (2 x) = \frac{3}{2}

What is the general solution for 8sin^2(x)-6=0 ?
The general solution for 8sin^2(x)-6=0 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin