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

The general solution for 2-2cos(x)=-6cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

2 sin^{2} (u) = 1 + sin (u), 0 \leq t < 2 π

tan (3 y + 60) tan (2 y + 5) = 1

1 8^{2} = 8^{2} + 2 0^{2} - 2 \cdot 8 \cdot 20 \cdot cos (x)

cot (θ) = - \frac{π}{6}

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

What is the general solution for 2-2cos(x)=-6cos(x) ?
The general solution for 2-2cos(x)=-6cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin