What is the general solution for 5cos(x)+2=cos(x) ?

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

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5cos(x)+2=cos(x)

5 cos (x) + 2 = cos (x)

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

Solution steps

5 cos (x) + 2 = 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 tan (4 x) + 1 = 3 tan (4 x)

sec (x) = - 5, π < x < \frac{3 π}{2}

sin (\frac{θ}{2}) = \frac{3}{5}

2 sin^{3} (t) + sin^{2} (t) - 2 sin (t) - 1 = 0

sin (x) = \frac{1}{5}, cos (x) > 0

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