erweitern tan^2(x)(csc(x)-1)^2

Lösung

erweitern

tan^{2} (x) (csc (x) - 1)^{2}

tan^{2} (x) csc^{2} (x) - 2 tan^{2} (x) csc (x) + tan^{2} (x)

Schritte zur Lösung

tan^{2} (x) (csc (x) - 1)^{2}

Schreibe

(csc (x) - 1)^{2}

um:

csc^{2} (x) - 2 csc (x) + 1

= tan^{2} (x) (csc^{2} (x) - 2 csc (x) + 1)

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

tan^{2} (x) (csc^{2} (x) - 2 csc (x) + 1) = tan^{2} (x) csc^{2} (x) + tan^{2} (x) (- 2 csc (x)) + tan^{2} (x) \cdot 1

= tan^{2} (x) csc^{2} (x) + tan^{2} (x) (- 2 csc (x)) + tan^{2} (x) \cdot 1

Vereinfache

tan^{2} (x) csc^{2} (x) + tan^{2} (x) (- 2 csc (x)) + tan^{2} (x) \cdot 1 : tan^{2} (x) csc^{2} (x) - 2 tan^{2} (x) csc (x) + tan^{2} (x)

= tan^{2} (x) csc^{2} (x) - 2 tan^{2} (x) csc (x) + tan^{2} (x)

e x p an d (tan (x) + tan (y)) cos (x) cos (y)

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

s im pl i f y (x) \cdot (x - 14)

e x p an d (cos (x))^{4}

e x p an d \frac{1}{( x - n ) ( x - na ) ( x - n a ^{2} )}