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

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

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2cos^2(t)=sin^2(t)

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

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

Solution steps

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

Subtract

sin^{2} (t)

from both sides

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

Show solutions in decimal form

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

5 sin (θ) + 3 = 3

sin (3 x) = 0, 0 < x \leq 2

tan (x) = - 0.35

0 = cos (2 t - \frac{π}{3})

sin (0.5 x) = 0

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