erweitern (1+cos(x))^4*sin(x)

Lösung

erweitern

(1 + cos (x))^{4} \cdot sin (x)

sin (x) + 4 cos (x) sin (x) + 6 cos^{2} (x) sin (x) + 4 cos^{3} (x) sin (x) + cos^{4} (x) sin (x)

Schritte zur Lösung

(1 + cos (x))^{4} sin (x)

= sin (x) (1 + cos (x))^{4}

Schreibe

(1 + cos (x))^{4}

um:

1 + 4 cos (x) + 6 cos^{2} (x) + 4 cos^{3} (x) + cos^{4} (x)

= sin (x) (1 + 4 cos (x) + 6 cos^{2} (x) + 4 cos^{3} (x) + cos^{4} (x))

Setze Klammern

= sin (x) \cdot 1 + sin (x) \cdot 4 cos (x) + sin (x) \cdot 6 cos^{2} (x) + sin (x) \cdot 4 cos^{3} (x) + sin (x) cos^{4} (x)

Vereinfache

sin (x) \cdot 1 + sin (x) \cdot 4 cos (x) + sin (x) \cdot 6 cos^{2} (x) + sin (x) \cdot 4 cos^{3} (x) + sin (x) cos^{4} (x) : sin (x) + 4 cos (x) sin (x) + 6 cos^{2} (x) sin (x) + 4 cos^{3} (x) sin (x) + cos^{4} (x) sin (x)

= sin (x) + 4 cos (x) sin (x) + 6 cos^{2} (x) sin (x) + 4 cos^{3} (x) sin (x) + cos^{4} (x) sin (x)

e x p an d \frac{1}{10} (e^{x} - e^{- x})

s im pl i f y x^{3} δ (x - 2)

e x p an d v (- 3, - 2) f (1, - 2)

s im pl i f y (A e^{i x} + B e^{- i x})^{2}

e x p an d (e^{iπ θ} - e^{- iπ θ})^{6}