What is the general solution for 2cos^2(x)-1+cos(x)=0 ?

The general solution for 2cos^2(x)-1+cos(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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2cos^2(x)-1+cos(x)=0

2 cos^{2} (x) - 1 + cos (x) = 0

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

Solution steps

2 cos^{2} (x) - 1 + cos (x) = 0

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

4 cot (θ) sin (θ) = 2

2 sin (2 x) - 5 tan (2 x) = 0

75 = \frac{120}{4} \cdot cos (\frac{2 \cdot π \cdot x}{360}) + \frac{120}{2}

cot^{2} (x) + 2 = 2 csc (x)

3 sin (x) + cos (x) = 2

What is the general solution for 2cos^2(x)-1+cos(x)=0 ?
The general solution for 2cos^2(x)-1+cos(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin