What is the general solution for 12cos^2(x)=3 ?

The general solution for 12cos^2(x)=3 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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12cos^2(x)=3

12 cos^{2} (x) = 3

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

12 cos^{2} (x) = 3

Solve by substitution

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

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

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{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

2 cos (x) - 2 sin (x) = 1, 0 \leq x < 2 π

sin (x) = 3 cos (x)

2 sin^{2} (x) - 3 cos (x) = 3

4 cos (x) = 3 + 8 cos (x)

sin^{2} (θ) - 3 sin (θ) = 0

What is the general solution for 12cos^2(x)=3 ?
The general solution for 12cos^2(x)=3 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin