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

The general solution for cos(2x)+1=-2cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin

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

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = π + 2 πn

Solution steps

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

Subtract

- 2 cos (x)

from both sides

cos (2 x) + 1 + 2 cos (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = - 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = π + 2 πn

sin (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

4 cos^{2} (x) + 2 cos (x) = 2, 0 \leq x \leq 2 π

arctan (x) + arctan (2 x) = \frac{π}{4}

1 + cos (θ) = \frac{2 + 3}{2}

1 + 3 sin (x) = 2

What is the general solution for cos(2x)+1=-2cos(x) ?
The general solution for cos(2x)+1=-2cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin