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

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

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2cos^2(x)= 1/2

2 cos^{2} (x) = \frac{1}{2}

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 cos^{2} (x) = \frac{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

2 sin (2 x + \frac{3 π}{2}) = 3

2 cos (θ) - 2 = 6 cos (θ)

10 sin^{2} (x) + 15 sin (x) + 5 = 0

3 sin (θ) - 1 = - 1

sin (x) = \frac{6.2}{8}

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