What is the general solution for 7cos(x)+4=-cos(x) ?

The general solution for 7cos(x)+4=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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7cos(x)+4=-cos(x)

7 cos (x) + 4 = - cos (x)

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

Solution steps

7 cos (x) + 4 = - 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} (θ) - sin (θ) - 1 = 0, 0 \leq θ < 2 π

3 sin (x) = tan (x)

cos^{2} (θ) + cos (θ) = sin^{2} (θ)

cos (4 x) = \frac{3}{2}

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

What is the general solution for 7cos(x)+4=-cos(x) ?
The general solution for 7cos(x)+4=-cos(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin