What is the general solution for sin^2(2x)= 3/4 ?

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

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sin^2(2x)= 3/4

sin^{2} (2 x) = \frac{3}{4}

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Solution steps

sin^{2} (2 x) = \frac{3}{4}

Solve by substitution

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

sin (2 x) = \frac{3}{2} : x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

sin (2 x) = - \frac{3}{2} : x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

sin (θ) = cos (13 0^{\circ})

2 sin^{2} (θ) - sin (θ) - 2 = 0

3 cot (x) + 2 = 5

sec^{2} (x) - tan (x) - 1 = 0

2 cos (2 x + \frac{π}{6}) + 3 = 2, 0 < x < 2 π

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