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

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

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sin^2(θ)=3cos^2(θ)

sin^{2} (θ) = 3 cos^{2} (θ)

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

Solution steps

sin^{2} (θ) = 3 cos^{2} (θ)

Subtract

3 cos^{2} (θ)

from both sides

sin^{2} (θ) - 3 cos^{2} (θ) = 0

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

20 sin^{2} (x) + 27 cos (x) = 6

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

arctan (x) = \frac{2.73}{7.5}

y, sin (x) + cos (y) = ln (x)

- 8 csc^{2} (x) - 4 cot (x) = - 12

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