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

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

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

solve for

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

x, - 2 sin (2 x) = 0

sin (θ) + cos (2 θ) = 1

- 6 sec (θ) - 3 = - 15

15 cos (θ) = 7 + cos (θ)

2 cos (3 x) = 2

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