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

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

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cos^2(x)-3/2 = 5/2 cos(x)

cos^{2} (x) - \frac{3}{2} = \frac{5}{2} cos (x)

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

Solution steps

cos^{2} (x) - \frac{3}{2} = \frac{5}{2} cos (x)

Solve by substitution

cos (x) = 3, cos (x) = - \frac{1}{2}

cos (x) = 3 :

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

θ, w = fd cos (θ)

sec (x) - sec (x) tan (x) = 0

4 sin^{2} (x) = 3, 0 \leq x \leq 18 0^{\circ}

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

(3 cos (x) + 2 sin (x))^{2} + 5 sin^{2} (x) = 9 - 33

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