What is the general solution for cos^4(x)-2sin^2(x)-1=0 ?

The general solution for cos^4(x)-2sin^2(x)-1=0 is x=2pin,x=pi+2pin

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cos^4(x)-2sin^2(x)-1=0

cos^{4} (x) - 2 sin^{2} (x) - 1 = 0

x = 2 πn, x = π + 2 πn

Solution steps

cos^{4} (x) - 2 sin^{2} (x) - 1 = 0

Rewrite using trig identities

- 3 + cos^{4} (x) + 2 cos^{2} (x) = 0

Solve by substitution

cos (x) = 1, cos (x) = - 1, cos (x) = 3 i, cos (x) = - 3 i

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = 3 i :

No Solution

cos (x) = - 3 i :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

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

cos^{4} (x) - 2 cos^{2} (x) + 1 = 0

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

\frac{sin ^{3} ( x )}{sin ( x )} = 0

sin (135 - x) = sin (x)

What is the general solution for cos^4(x)-2sin^2(x)-1=0 ?
The general solution for cos^4(x)-2sin^2(x)-1=0 is x=2pin,x=pi+2pin