What is the general solution for 11cos(x)+6=-cos(x) ?

The general solution for 11cos(x)+6=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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11cos(x)+6=-cos(x)

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

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

Solution steps

11 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

cos^{2} (x) = 8 sin^{2} (x) - 6 sin (x)

3 sin (x) - cos (x) = 1

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

(csc (θ) - 2) (cot (θ) + 1) = 0

sin (x) = csc (x)

What is the general solution for 11cos(x)+6=-cos(x) ?
The general solution for 11cos(x)+6=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin