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

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

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

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

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

Solution steps

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

Subtract

3 cos^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

sin (- π)

cos (5)

2 sin^{2} (θ) + cos (θ) = 1, 0 \leq θ \leq 2 π

sin (- \frac{5 π}{3})

cos (4)

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