What is the general solution for 2=4cos^2(x)+1 ?

The general solution for 2=4cos^2(x)+1 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2=4cos^2(x)+1

2 = 4 cos^{2} (x) + 1

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

2 = 4 cos^{2} (x) + 1

Switch sides

4 cos^{2} (x) + 1 = 2

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

1 - sin^{2} (x) = 0

sin (\frac{x}{2}) = - \frac{1}{2}

cot (x) + 1 = csc (x)

2 cos^{2} (x) + 4 sin^{2} (x) = 3

x, sin (x) = 1

What is the general solution for 2=4cos^2(x)+1 ?
The general solution for 2=4cos^2(x)+1 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin