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

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

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2cos^2(x)=cos(x)

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

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

Solution steps

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

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = 0

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

sin (y) = 0

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

tan (θ) = \frac{3}{2}

sin (x) + 3 cos (x) = 0

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

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