What is the general solution for 3cos(2x)=4-11cos(x) ?

The general solution for 3cos(2x)=4-11cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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3cos(2x)=4-11cos(x)

3 cos (2 x) = 4 - 11 cos (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

3 cos (2 x) = 4 - 11 cos (x)

Subtract

4 - 11 cos (x)

from both sides

3 cos (2 x) - 4 + 11 cos (x) = 0

Rewrite using trig identities

- 7 + 11 cos (x) + 6 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = - \frac{7}{3}

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - \frac{7}{3} :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x, 2 cos^{2} (x) - cos (x) = 0

8 tan (2 x) - 5 = 3

- 8 cos (x) = 3

tan (x) \cdot cos (x) + cos (x) = 0

2 sin (3 x) - 1 = 0

What is the general solution for 3cos(2x)=4-11cos(x) ?
The general solution for 3cos(2x)=4-11cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin