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

The general solution for sin^2(x)-tan(x)cos^2(x)=0 is x=2pin,x=pi+2pin,x= pi/4+pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) - cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

2 sin (x) cos (x) - sin (x) + 2 cos (x) - 1 = 0

sec^{2} (x) = 2 tan (x)

4 sin^{2} (x) - 8 cos (x) + 1 = 0

sec^{2} (θ) = 4

sin (a) = \frac{5}{13}

What is the general solution for sin^2(x)-tan(x)cos^2(x)=0 ?
The general solution for sin^2(x)-tan(x)cos^2(x)=0 is x=2pin,x=pi+2pin,x= pi/4+pin