What is the general solution for solvefor x,-4cos(x)-4cos(2x)=0 ?

The general solution for solvefor x,-4cos(x)-4cos(2x)=0 is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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solvefor x,-4cos(x)-4cos(2x)=0

solve for

x, - 4 cos (x) - 4 cos (2 x) = 0

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

Solution steps

- 4 cos (x) - 4 cos (2 x) = 0

Rewrite using trig identities

- (- 1 + 2 cos^{2} (x)) \cdot 4 - 4 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

3 - 2 cos (x) = 3 - 2 sin (x)

3 sin (x) = sin (x) tan (x)

- 2 sin (2 y) = 0

- 3 + 4 (cos^{2} (x))^{2} + 3 sin^{2} (x) = 0

4 sin (x - 3 0^{\circ}) - 1.3 = 0

What is the general solution for solvefor x,-4cos(x)-4cos(2x)=0 ?
The general solution for solvefor x,-4cos(x)-4cos(2x)=0 is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin