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

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

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

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

x = π + 2 πn

Solution steps

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

Subtract

2

from both sides

cos (2 x) - cos (x) - 2 = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = \frac{3}{2}, cos (x) = - 1

cos (x) = \frac{3}{2} :

No Solution

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

4 sin (2 x) + 23 = 0

x, 3 = 18 cos (x)

x, 2 sin (\frac{π ( x - 2 )}{6}) = 1

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

2 cos (x) = cos^{2} (x) - 1

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