erweitern (tan^2(12x)-cot^2(12x))^2

Lösung

erweitern

(tan^{2} (12 x) - cot^{2} (12 x))^{2}

tan^{4} (12 x) - 2 tan^{2} (12 x) cot^{2} (12 x) + cot^{4} (12 x)

Schritte zur Lösung

(tan^{2} (12 x) - cot^{2} (12 x))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(tan^{2} (12 x) - cot^{2} (12 x))^{2} = (tan^{2} (12 x))^{2} - 2 tan^{2} (12 x) cot^{2} (12 x) + (cot^{2} (12 x))^{2}

= (tan^{2} (12 x))^{2} - 2 tan^{2} (12 x) cot^{2} (12 x) + (cot^{2} (12 x))^{2}

Vereinfache

(tan^{2} (12 x))^{2} - 2 tan^{2} (12 x) cot^{2} (12 x) + (cot^{2} (12 x))^{2} : tan^{4} (12 x) - 2 tan^{2} (12 x) cot^{2} (12 x) + cot^{4} (12 x)

= tan^{4} (12 x) - 2 tan^{2} (12 x) cot^{2} (12 x) + cot^{4} (12 x)

e x p an d (e^{y} - e^{- y})^{2}

e x p an d 43 (35 + 2)

e x p an d 2 y d y - (3 y^{2} cot (x) - sin (x) cos (x)) d x

e x p an d (16 x y - 3 x^{2}) d x + (8 x^{2} + 2 y) d y

e x p an d cos (2 t) u (t - π)