What is the general solution for cos(2x)+sqrt(3)cos(x)=2 ?

The general solution for cos(2x)+sqrt(3)cos(x)=2 is x= pi/6+2pin,x=(11pi)/6+2pin

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cos(2x)+sqrt(3)cos(x)=2

cos (2 x) + 3 cos (x) = 2

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

cos (2 x) + 3 cos (x) = 2

Subtract

2

from both sides

cos (2 x) + 3 cos (x) - 2 = 0

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

cos (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

6 sin (x) + 1 = 0

π + 3 arccos (x + 1) = 0

5 sin (2 x) + 3 cos (2 x) = 0

x, sin (2 x) - sin (x) = 0

x, sin (x^{e}) + cos (y^{e}) = 1

What is the general solution for cos(2x)+sqrt(3)cos(x)=2 ?
The general solution for cos(2x)+sqrt(3)cos(x)=2 is x= pi/6+2pin,x=(11pi)/6+2pin