What is the general solution for 2cos^2(a)-3cos(a)+1=0 ?

The general solution for 2cos^2(a)-3cos(a)+1=0 is a=2pin,a= pi/3+2pin,a=(5pi)/3+2pin

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2cos^2(a)-3cos(a)+1=0

2 cos^{2} (a) - 3 cos (a) + 1 = 0

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

Solution steps

2 cos^{2} (a) - 3 cos (a) + 1 = 0

Solve by substitution

cos (a) = 1, cos (a) = \frac{1}{2}

cos (a) = 1 : a = 2 πn

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

Combine all the solutions

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

sin (x) \cdot cos (2 x) = 0.5 - sin (2 x) \cdot cos (x)

tan (x) = 0.625

4 sin^{2} (2 θ) + 6 = 9

tan (a) = \frac{1}{3}

tan (x) = 0.649

What is the general solution for 2cos^2(a)-3cos(a)+1=0 ?
The general solution for 2cos^2(a)-3cos(a)+1=0 is a=2pin,a= pi/3+2pin,a=(5pi)/3+2pin