What is the general solution for 2cos^2(a)=1+cos(120) ?

The general solution for 2cos^2(a)=1+cos(120) is a=60+360n,a=300+360n,a=120+360n,a=240+360n

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2cos^2(a)=1+cos(120)

2 cos^{2} (a) = 1 + cos (12 0^{\circ})

a = 6 0^{\circ} + 36 0^{\circ} n, a = 30 0^{\circ} + 36 0^{\circ} n, a = 12 0^{\circ} + 36 0^{\circ} n, a = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

2 cos^{2} (a) = 1 + cos (12 0^{\circ})

cos (12 0^{\circ}) = - \frac{1}{2}

2 cos^{2} (a) = 1 + - \frac{1}{2}

Solve by substitution

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

cos (a) = \frac{1}{2} : a = 6 0^{\circ} + 36 0^{\circ} n, a = 30 0^{\circ} + 36 0^{\circ} n

cos (a) = - \frac{1}{2} : a = 12 0^{\circ} + 36 0^{\circ} n, a = 24 0^{\circ} + 36 0^{\circ} n

Combine all the solutions

a = 6 0^{\circ} + 36 0^{\circ} n, a = 30 0^{\circ} + 36 0^{\circ} n, a = 12 0^{\circ} + 36 0^{\circ} n, a = 24 0^{\circ} + 36 0^{\circ} n

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

4 = 5 + 3 sin (2 t - \frac{π}{5})

sin^{2} (2 x) + 2 \cdot cos^{2} (x) - 2 = 0

What is the general solution for 2cos^2(a)=1+cos(120) ?
The general solution for 2cos^2(a)=1+cos(120) is a=60+360n,a=300+360n,a=120+360n,a=240+360n