What is the general solution for 1-3cos(x)-cos(2x)=0 ?

The general solution for 1-3cos(x)-cos(2x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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1-3cos(x)-cos(2x)=0

1 - 3 cos (x) - cos (2 x) = 0

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

Solution steps

1 - 3 cos (x) - cos (2 x) = 0

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 2 :

No Solution

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

Combine all the solutions

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

cot (θ) = \frac{12}{5}, tan (θ)

sin (a) = cos (\frac{π}{2} - θ)

tan (θ) + sec (θ) = 2 cos (θ)

cos (x) = 0.68

cos (x) = 0.65

What is the general solution for 1-3cos(x)-cos(2x)=0 ?
The general solution for 1-3cos(x)-cos(2x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin