What is the general solution for cos^2(x)-5/2 cos(x)-3/2 =0 ?

The general solution for cos^2(x)-5/2 cos(x)-3/2 =0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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cos^2(x)-5/2 cos(x)-3/2 =0

cos^{2} (x) - \frac{5}{2} cos (x) - \frac{3}{2} = 0

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

Solution steps

cos^{2} (x) - \frac{5}{2} cos (x) - \frac{3}{2} = 0

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

x, sin (4 x) = \frac{1}{2}

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

7 sec (x) - 7 = 0, 0 \leq x \leq 2 π

cos (x) + cos (x) = cos (2 x)

csc^{2} (2 x - 0.6) = 16

What is the general solution for cos^2(x)-5/2 cos(x)-3/2 =0 ?
The general solution for cos^2(x)-5/2 cos(x)-3/2 =0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin