What is the general solution for 2sin^2(x)=6cos^2(x) ?

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

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2sin^2(x)=6cos^2(x)

2 sin^{2} (x) = 6 cos^{2} (x)

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

Solution steps

2 sin^{2} (x) = 6 cos^{2} (x)

Subtract

6 cos^{2} (x)

from both sides

2 sin^{2} (x) - 6 cos^{2} (x) = 0

Factor

2 sin^{2} (x) - 6 cos^{2} (x) : 2 (sin (x) + 3 cos (x)) (sin (x) - 3 cos (x))

2 (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

1 + cot^{2} (θ) = 1.33

x, r + s - 6 t = cos (2 x + y)

cos (x) + cos^{3} (x) = 0

- 2 cos (\frac{θ}{2}) = 0

cos (x) = - \frac{3}{4}, tan (x) i s

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