What is the general solution for sin^2(a)=3cos^2(a) ?

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

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sin^2(a)=3cos^2(a)

sin^{2} (a) = 3 cos^{2} (a)

a = \frac{2 π}{3} + πn, a = \frac{π}{3} + πn

Solution steps

sin^{2} (a) = 3 cos^{2} (a)

Subtract

3 cos^{2} (a)

from both sides

sin^{2} (a) - 3 cos^{2} (a) = 0

Factor

sin^{2} (a) - 3 cos^{2} (a) : (sin (a) + 3 cos (a)) (sin (a) - 3 cos (a))

(sin (a) + 3 cos (a)) (sin (a) - 3 cos (a)) = 0

Solving each part separately

sin (a) + 3 cos (a) = 0 or sin (a) - 3 cos (a) = 0

sin (a) + 3 cos (a) = 0 : a = \frac{2 π}{3} + πn

sin (a) - 3 cos (a) = 0 : a = \frac{π}{3} + πn

Combine all the solutions

a = \frac{2 π}{3} + πn, a = \frac{π}{3} + πn

3 cot (x) + 3 = 0

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

sec (2 x) + 2 = 0

3 sin (x + 2 0^{\circ}) - 0.75 = 0

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

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