What is the general solution for cos^2(2x)-2sin^2(x)-1=0 ?

The general solution for cos^2(2x)-2sin^2(x)-1=0 is x=pin

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cos^2(2x)-2sin^2(x)-1=0

cos^{2} (2 x) - 2 sin^{2} (x) - 1 = 0

x = πn

Solution steps

cos^{2} (2 x) - 2 sin^{2} (x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

cos (2 x) = 1, cos (2 x) = - 2

cos (2 x) = 1 : x = πn

cos (2 x) = - 2 :

No Solution

Combine all the solutions

x = πn

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

- sin (2 x) - 3 cos (x) = 0

x, y = 3 cos (f xx + \frac{π}{2}) + 5

sin (x) cos (x) = sin (x), 0 < x \leq 2 π

cos^{5} (x) - sin (x) = 0

What is the general solution for cos^2(2x)-2sin^2(x)-1=0 ?
The general solution for cos^2(2x)-2sin^2(x)-1=0 is x=pin