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

The general solution for cos^2(x)=3sin^2(x) is x=(5pi)/6+pin,x= pi/6+pin

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

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

x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

Solution steps

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

Subtract

3 sin^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

cos (x) + 3 sin (x) = 0 : x = \frac{5 π}{6} + πn

cos (x) - 3 sin (x) = 0 : x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

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

- 4 arctan (x) = π

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

sin (x) = - \frac{3}{2}, 0 \leq x \leq 2 π

sin^{2} (x) = 1 + cos^{2} (x)

What is the general solution for cos^2(x)=3sin^2(x) ?
The general solution for cos^2(x)=3sin^2(x) is x=(5pi)/6+pin,x= pi/6+pin