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

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

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

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

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

Solution steps

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

Subtract

cos^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

sec (arcsin (- \frac{2}{2}))

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

sec (21 0^{\circ})

tan (x) + cot (x) = sec (x) csc (x)

sec (\frac{7 π}{6})

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