What is the general solution for 5cos(x)+2sqrt(3)=cos(x) ?

The general solution for 5cos(x)+2sqrt(3)=cos(x) is x=(5pi)/6+2pin,x=(7pi)/6+2pin

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5cos(x)+2sqrt(3)=cos(x)

5 cos (x) + 23 = cos (x)

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solution steps

5 cos (x) + 23 = cos (x)

Solve by substitution

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

cos (x) = - \frac{3}{2} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Combine all the solutions

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

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

tan^{2} (θ) = 3 tan (θ)

4 sin^{2} (2) cot (x) - 2 = 0

5 sin (2 θ) + 2 sin (θ) = 0

cos^{2} (x) = \frac{19}{20}

What is the general solution for 5cos(x)+2sqrt(3)=cos(x) ?
The general solution for 5cos(x)+2sqrt(3)=cos(x) is x=(5pi)/6+2pin,x=(7pi)/6+2pin