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

The general solution for cos^{(2)}(x)-3sin^{(2)}(x)=0 is x=(5pi)/6+pin,x= pi/6+pin

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

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

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

Solution steps

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

a, cos (a) cos (b) = 0.426

5 cos (x) - 4 = 0

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

sin (x) = 14

tan (x) = 0, 5

What is the general solution for cos^{(2)}(x)-3sin^{(2)}(x)=0 ?
The general solution for cos^{(2)}(x)-3sin^{(2)}(x)=0 is x=(5pi)/6+pin,x= pi/6+pin