erweitern (sec(x)-1)^3

Lösung

erweitern

(sec (x) - 1)^{3}

sec^{3} (x) - 3 sec^{2} (x) + 3 sec (x) - 1

Schritte zur Lösung

(sec (x) - 1)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(sec (x) - 1)^{3} = sec^{3} (x) - 3 sec^{2} (x) \cdot 1 + 3 sec (x) \cdot 1^{2} - 1^{3}

= sec^{3} (x) - 3 sec^{2} (x) \cdot 1 + 3 sec (x) \cdot 1^{2} - 1^{3}

Vereinfache

sec^{3} (x) - 3 sec^{2} (x) \cdot 1 + 3 sec (x) \cdot 1^{2} - 1^{3} : sec^{3} (x) - 3 sec^{2} (x) + 3 sec (x) - 1

= sec^{3} (x) - 3 sec^{2} (x) + 3 sec (x) - 1

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

s im pl i f y (2 x + 3 y) (4 x + 5 y)

e x p an d (cos (x) e n (x) - x y^{2}) \cdot 1 - x^{2}^{- 1 + y}

e x p an d \frac{2 ( x ^{5} - 12 )}{x ^{4}}

e x p an d 2 (- 3 - 3)