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

The general solution for sin^2(x)-2=cos(2x) is x= pi/2+2pin,x=(3pi)/2+2pin

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

sin^{2} (x) - 2 = cos (2 x)

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

Solution steps

sin^{2} (x) - 2 = cos (2 x)

Subtract

cos (2 x)

from both sides

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

Rewrite using trig identities

- 3 + 3 sin^{2} (x) = 0

Solve by substitution

sin (x) = 1, sin (x) = - 1

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

cos (x + \frac{3 π}{2}) + 2 sin (x + π) = 0

3 + 6 sin (3 x) = 0

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

θ, x = 5 tan (θ)

cos (x) tan (x) cos (x) = 0, 0 \leq x \leq 2 π

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