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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Setze Klammern

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

Vereinfache

1 \cdot 1 + 1 \cdot sin (x) + 1 \cdot (- cos (x)) + sin (x) \cdot 1 + sin (x) sin (x) + sin (x) (- cos (x)) - cos (x) \cdot 1 - cos (x) sin (x) - cos (x) (- cos (x)) : 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}{( x ^{2} y ^{2} + x ^{2} z ^{2} ) x}

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

e x p an d (- a sin (z) y + b cos (z)) \cdot 2 r sin (z)

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

e x p an d (1 - sec (2 x))^{2}