erweitern (1+tan(x))^3sec^2(x)

Lösung

erweitern

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

sec^{2} (x) + 3 sec^{2} (x) tan (x) + 3 sec^{2} (x) tan^{2} (x) + sec^{2} (x) tan^{3} (x)

Schritte zur Lösung

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

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

Schreibe

(1 + tan (x))^{3}

um:

1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x)

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

Setze Klammern

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

Vereinfache

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

= sec^{2} (x) + 3 sec^{2} (x) tan (x) + 3 sec^{2} (x) tan^{2} (x) + sec^{2} (x) tan^{3} (x)

e x p an d (x^{\frac{1}{2}} + 1) (x^{\frac{1}{2}} - 1)

e x p an d (x - 4) \cdot (x + 2)

e x p an d \frac{9 x + 25}{( x + 3 ) ^{2}}

e x p an d \frac{x + 2}{( x + 3 ) ( x - 1 )}

e x p an d \frac{e ^{- 6 s}}{( s - 5 ) ^{2}}