What is the general solution for 6cos(x)=-6(1+cos(x)) ?

The general solution for 6cos(x)=-6(1+cos(x)) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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6cos(x)=-6(1+cos(x))

6 cos (x) = - 6 (1 + cos (x))

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

Solution steps

6 cos (x) = - 6 (1 + 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

sin (θ) = \frac{60 sin ( 1 5 ^{\circ} )}{400}

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

2 cos^{2} (θ) + 2 cos (θ) = 0

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

cos (2 x) + 5 sin (x) + 2 = 0, 0 \leq x \leq 2 π

What is the general solution for 6cos(x)=-6(1+cos(x)) ?
The general solution for 6cos(x)=-6(1+cos(x)) is x=(2pi)/3+2pin,x=(4pi)/3+2pin