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

The general solution for cos^2(x)=2sin^2(x) is x=-0.61547…+pin,x=0.61547…+pin

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

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

x = - 0.61547 \dots + πn, x = 0.61547 \dots + πn

Solution steps

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

Subtract

2 sin^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

cos (x) + 2 sin (x) = 0 : x = arctan (- \frac{2}{2}) + πn

cos (x) - 2 sin (x) = 0 : x = arctan (\frac{2}{2}) + πn

Combine all the solutions

x = arctan (- \frac{2}{2}) + πn, x = arctan (\frac{2}{2}) + πn

Show solutions in decimal form

x = - 0.61547 \dots + πn, x = 0.61547 \dots + πn

x, sec (x) - sin (50 o) = 2

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

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

x, cos^{2} (x) + cos^{2} (y) cos^{2} (z) = 1

cos (5 x) + cos (x) = 0

What is the general solution for cos^2(x)=2sin^2(x) ?
The general solution for cos^2(x)=2sin^2(x) is x=-0.61547…+pin,x=0.61547…+pin