What is the general solution for sin^2(2x)=0.5 ?

The general solution for sin^2(2x)=0.5 is x= pi/8+pin,x= pi/2-pi/8+pin,x=-pi/8+pin,x= pi/2+pi/8+pin

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sin^2(2x)=0.5

sin^{2} (2 x) = 0.5

x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn, x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

Solution steps

sin^{2} (2 x) = 0.5

Solve by substitution

sin (2 x) = 0.5, sin (2 x) = - 0.5

sin (2 x) = 0.5 : x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn

sin (2 x) = - 0.5 : x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

Combine all the solutions

x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn, x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

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

(6 cos (x) + 5 sin (x))^{2} + 11 sin^{2} (x) = 66

- 3 sin (B) - 2 = sin (B) - 2

sin (\frac{θ}{2}) = 2 - sin (\frac{θ}{2})

2 sin (x) cos (x) = cos (2 x)

What is the general solution for sin^2(2x)=0.5 ?
The general solution for sin^2(2x)=0.5 is x= pi/8+pin,x= pi/2-pi/8+pin,x=-pi/8+pin,x= pi/2+pi/8+pin