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

The general solution for 2*cos^2(x)-sin^2(x)=0 is x=-0.95531…+pin,x=0.95531…+pin

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2*cos^2(x)-sin^2(x)=0

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

x = - 0.95531 \dots + πn, x = 0.95531 \dots + πn

Solution steps

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

Factor

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

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

Solving each part separately

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

2 cos (x) + sin (x) = 0 : x = arctan (- 2) + πn

2 cos (x) - sin (x) = 0 : x = arctan (2) + πn

Combine all the solutions

x = arctan (- 2) + πn, x = arctan (2) + πn

Show solutions in decimal form

x = - 0.95531 \dots + πn, x = 0.95531 \dots + πn

cos (θ) = - \frac{35}{6}

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

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

2 sin (2 x) = 0

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

What is the general solution for 2*cos^2(x)-sin^2(x)=0 ?
The general solution for 2*cos^2(x)-sin^2(x)=0 is x=-0.95531…+pin,x=0.95531…+pin