What is the general solution for 9cos(x)+5=-cos(x) ?

The general solution for 9cos(x)+5=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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9cos(x)+5=-cos(x)

9 cos (x) + 5 = - cos (x)

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

Solution steps

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

tan (θ) = \frac{1}{4}

tan (θ) = \frac{1}{3}

2 sec (x) + 2 = 0

6 sin (θ) - 3 = 0

What is the general solution for 9cos(x)+5=-cos(x) ?
The general solution for 9cos(x)+5=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin