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

The general solution for sin^2(x)=2tan^2(x) is x=2pin,x=pi+2pin

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sin^2(x)=2tan^2(x)

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

2 tan^{2} (x)

from both sides

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

Factor

sin^{2} (x) - 2 tan^{2} (x) : (sin (x) + 2 tan (x)) (sin (x) - 2 tan (x))

(sin (x) + 2 tan (x)) (sin (x) - 2 tan (x)) = 0

Solving each part separately

sin (x) + 2 tan (x) = 0 or sin (x) - 2 tan (x) = 0

sin (x) + 2 tan (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) - 2 tan (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos^{3} (x) = cos (2 x + x)

x, (d^{2} - 3 d + 2) y = sin (e^{x})

cos (6 x) + cos (2 x) = 0

2 sin^{2} (4 5^{\circ} - a) = 1 - sin^{2} (a)

(2 cos (a) + 1) (2 cos (a) - 1) = 2 cos^{2} (a) + 1

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