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

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

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

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

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

Solution steps

2 - 3 cos (x) = 5 + 3 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

sinh (x) = \frac{6}{5}

tan (2 x) tan (x) = 1

\frac{csc ^{2} ( x )}{4} = 4 sin^{2} (x)

6 sec^{2} (x) - 3 cos (x) - 10 = sec (x)

1 + 4 cos (θ) = 3 sin (θ)

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