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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

4 - 2 sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Divide both sides by

- 2

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

sin (x) = 2 cos (\frac{x}{2})

2 sin (x) + \frac{1}{sin ( x )} = 3

cos (x - \frac{π}{4}) = \frac{3}{2}

sec (θ) = 3, sin (θ) < 0

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

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