What is the general solution for 4cos^2(x)-8cos(x)+3=0 ?

The general solution for 4cos^2(x)-8cos(x)+3=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos^2(x)-8cos(x)+3=0

4 cos^{2} (x) - 8 cos (x) + 3 = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

4 cos^{2} (x) - 8 cos (x) + 3 = 0

Solve by substitution

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

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

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (2 x) = - 0.6

\frac{11}{sin ( 9 0 ^{\circ} )} = \frac{10}{sin ( x )}

2 sec^{2} (x) + 4 tan (x) = 1

8 sin (\frac{3.14}{4 \cdot x}) = 7

cos (3 x) - 21 cos (x) + 16 = 0

What is the general solution for 4cos^2(x)-8cos(x)+3=0 ?
The general solution for 4cos^2(x)-8cos(x)+3=0 is x= pi/3+2pin,x=(5pi)/3+2pin