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

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

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

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

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

Solution steps

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

Rewrite using trig identities

- (- 1 + 2 cos^{2} (x)) \cdot 2 - 2 cos (x) = 0

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

tan^{2} (x) + 4 tan (x) + 2 = 0

- 9 sin^{2} (θ) + 4 = 5 cos (θ) - 1

tan (θ) = 1.25

6 sec (θ) + 6 = 0

2 sin (θ) - 2 = 0

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