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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

sin (2 x) + sin (x) = 0, 0 \leq x \leq 2 π

cos (2 t) = 0

sec (5 x) - 2 = 0

sin (z) = 0

4 sec (x) + 4 tan (x) = 4

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