What is the general solution for 2cos^2(a)-7cos(a)+3=0 ?

The general solution for 2cos^2(a)-7cos(a)+3=0 is a= pi/3+2pin,a=(5pi)/3+2pin

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2cos^2(a)-7cos(a)+3=0

2 cos^{2} (a) - 7 cos (a) + 3 = 0

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

Solution steps

2 cos^{2} (a) - 7 cos (a) + 3 = 0

Solve by substitution

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

cos (a) = 3 :

No Solution

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

Combine all the solutions

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

y, x = 2 cos (2 y)

- 3 - 6 cos (x) = 0

tan (θ) = \frac{26}{53}

n, y = - sin (2 (\frac{π}{4} + πn)) 2

tan (a) = \frac{7}{24}

What is the general solution for 2cos^2(a)-7cos(a)+3=0 ?
The general solution for 2cos^2(a)-7cos(a)+3=0 is a= pi/3+2pin,a=(5pi)/3+2pin