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

The general solution for -1-2cos(x)=-cos(x) is x=pi+2pin

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

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

x = π + 2 πn

Degrees

x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Solve by substitution

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

Let:

cos (x) = u

- 1 - 2 u = - u

- 1 - 2 u = - u : u = - 1

- 1 - 2 u = - u

Move

1

to the right side

- 1 - 2 u = - u

Add

1

to both sides

- 1 - 2 u + 1 = - u + 1

Simplify

- 2 u = - u + 1

- 2 u = - u + 1

Move

u

to the left side

- 2 u = - u + 1

Add

u

to both sides

- 2 u + u = - u + 1 + u

Simplify

- u = 1

- u = 1

Divide both sides by

- 1

- u = 1

Divide both sides by

- 1

\frac{- u}{- 1} = \frac{1}{- 1}

Simplify

u = - 1

u = - 1

Substitute back

u = cos (x)

cos (x) = - 1

cos (x) = - 1

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

General solutions for

cos (x) = - 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = π + 2 πn

x = π + 2 πn

Combine all the solutions

x = π + 2 πn

x, arctan (\frac{y}{x}) = 45

cos (H) = 0.3648447229

θ, cos (\frac{θ}{2} + 3 0^{\circ}) = sin (θ)

5 sin^{2} (θ) = 1 + 3 sin^{2} (θ)

5 sin (2 θ) - 8 sin (θ) = 0

What is the general solution for -1-2cos(x)=-cos(x) ?
The general solution for -1-2cos(x)=-cos(x) is x=pi+2pin