erweitern (cos(x)-sin(x)-1)^2

Lösung

erweitern

(cos (x) - sin (x) - 1)^{2}

2 sin (x) - 2 cos (x) - sin (2 x) + 2

Schritte zur Lösung

(cos (x) - sin (x) - 1)^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(cos (x) - sin (x) - 1)^{2} = (cos (x) - sin (x) - 1) (cos (x) - sin (x) - 1)

= (cos (x) - sin (x) - 1) (cos (x) - sin (x) - 1)

Setze Klammern

= cos (x) cos (x) + cos (x) (- sin (x)) + cos (x) (- 1) - sin (x) cos (x) - sin (x) (- sin (x)) - sin (x) (- 1) - 1 \cdot cos (x) - 1 \cdot (- sin (x)) - 1 \cdot (- 1)

Vereinfache

cos (x) cos (x) + cos (x) (- sin (x)) + cos (x) (- 1) - sin (x) cos (x) - sin (x) (- sin (x)) - sin (x) (- 1) - 1 \cdot cos (x) - 1 \cdot (- sin (x)) - 1 \cdot (- 1) : 2 sin (x) - 2 cos (x) - sin (2 x) + 2

= 2 sin (x) - 2 cos (x) - sin (2 x) + 2

e x p an d \frac{1}{s ( s + 5 ) ^{3}}

e x p an d 2 x (2 x + 1)

e x p an d \frac{8 x}{( x ^{2} + 4 ) ^{2}}

e x p an d (\frac{5}{8} x + y^{5}) (y^{5} - \frac{5}{8} x)

e x p an d \frac{5}{x ( x + 3 )}