What is the general solution for cos^{22}(x)-2sin^2(x)-1=0 ?

The general solution for cos^{22}(x)-2sin^2(x)-1=0 is x=2pin,x=pi+2pin

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cos^{22}(x)-2sin^2(x)-1=0

cos^{22} (x) - 2 sin^{2} (x) - 1 = 0

x = 2 πn, x = π + 2 πn

Solution steps

cos^{22} (x) - 2 sin^{2} (x) - 1 = 0

Rewrite using trig identities

- 3 + cos^{22} (x) + 2 cos^{2} (x) = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

tan (θ) = \frac{3 5}{2}

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

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

sin (3 x) = sin^{2} (x)

2 cot (x) + 3 = 0

What is the general solution for cos^{22}(x)-2sin^2(x)-1=0 ?
The general solution for cos^{22}(x)-2sin^2(x)-1=0 is x=2pin,x=pi+2pin