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

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

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

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

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

Solution steps

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

cos (2 x + \frac{π}{3}) = sin (3 x)

y, x = arcsin (y)

2 sin^{2} (x) + 5 sin (x) = 3

∣ sin (x) ∣ = \frac{1}{2}

sec^{2} (θ) = 2 tan (θ)

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