What is the general solution for 3cos(x)+9/2 =5+4cos(x) ?

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

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3cos(x)+9/2 =5+4cos(x)

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

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

Solution steps

3 cos (x) + \frac{9}{2} = 5 + 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

sec (2 x) + 2 = 0

3 sin (x + 2 0^{\circ}) - 0.75 = 0

2 sin^{2} (x) + sin (x) - 5 = 0

- 4 sin (x) = 4 (sin (x) - 1)

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

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