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

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

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2cos^2(x)=3cos(x)+2

2 cos^{2} (x) = 3 cos (x) + 2

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

Solution steps

2 cos^{2} (x) = 3 cos (x) + 2

Solve by substitution

cos (x) = 2, cos (x) = - \frac{1}{2}

cos (x) = 2 :

No Solution

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

sin (3 0^{\circ}) = cos (2 x)

tan (2 x) sin (x) - sin (x) - tan (2 x) + 1 = 0

3 sec (x) - cos (x) - 2 = 0

- 2 sin (t) = - 2

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

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