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

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

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

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

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

Solution steps

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

0 = 4 sin (2 x)

\frac{sin ( 112. 8 ^{\circ} )}{16.1} = \frac{sin ( x )}{12.2}

(sin (x) + cos (x))^{2} = \frac{3}{2}

2 sin^{2} (t) - sin (t) - 1 = 0

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