What is the general solution for 6cos(2x)=-6cos(x) ?

The general solution for 6cos(2x)=-6cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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6cos(2x)=-6cos(x)

6 cos (2 x) = - 6 cos (x)

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

Solution steps

6 cos (2 x) = - 6 cos (x)

Subtract

- 6 cos (x)

from both sides

6 cos (2 x) + 6 cos (x) = 0

Rewrite using trig identities

(- 1 + 2 cos^{2} (x)) \cdot 6 + 6 cos (x) = 0

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

3 sec (2 θ) = 2

2 sin^{2} (x) + 3 sin (x) - 1 = 0

- 6 cos^{2} (θ) + cos (θ) + 7 = 5

y, arccot (x y) = ln (sin (x))

tan (α) = - \frac{3}{4}

What is the general solution for 6cos(2x)=-6cos(x) ?
The general solution for 6cos(2x)=-6cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin