What is the general solution for 3sin^2(θ)-cos^2(θ)=0 ?

The general solution for 3sin^2(θ)-cos^2(θ)=0 is θ=(5pi)/6+pin,θ= pi/6+pin

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3sin^2(θ)-cos^2(θ)=0

3 sin^{2} (θ) - cos^{2} (θ) = 0

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

Solution steps

3 sin^{2} (θ) - cos^{2} (θ) = 0

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

2 cot (θ) - 3 = 0

\frac{1}{2} = cos (θ)

\frac{sin ( 2 x )}{1 - cos ( 2 x )} = 1

sin (2 x) cos (x) - sin (x) = 0

9 sec^{2} (x) - 12 = 0

What is the general solution for 3sin^2(θ)-cos^2(θ)=0 ?
The general solution for 3sin^2(θ)-cos^2(θ)=0 is θ=(5pi)/6+pin,θ= pi/6+pin