erweitern sin^2(x)(cot(x)+1)^2

Lösung

erweitern

sin^{2} (x) (cot (x) + 1)^{2}

sin^{2} (x) csc^{2} (x) + 2 sin^{2} (x) cot (x)

Schritte zur Lösung

sin^{2} (x) (cot (x) + 1)^{2}

Schreibe

(cot (x) + 1)^{2}

um:

cot^{2} (x) + 2 cot (x) + 1

= sin^{2} (x) (cot^{2} (x) + 2 cot (x) + 1)

Wende das Distributivgesetz an:

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

sin^{2} (x) (cot^{2} (x) + 2 cot (x) + 1) = sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1

= sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1

Vereinfache

sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1 : sin^{2} (x) (csc^{2} (x) + 2 cot (x))

= sin^{2} (x) (csc^{2} (x) + 2 cot (x))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

sin^{2} (x) (csc^{2} (x) + 2 cot (x)) = sin^{2} (x) csc^{2} (x) + sin^{2} (x) \cdot 2 cot (x)

= sin^{2} (x) csc^{2} (x) + sin^{2} (x) \cdot 2 cot (x)

= sin^{2} (x) csc^{2} (x) + 2 sin^{2} (x) cot (x)

e x p an d \frac{1}{x ( x ^{2} + 5 )}

e x p an d - (\frac{2 ( 2 s + 11 )}{( s ( s + 5 ) )})

e x p an d - \frac{5 ( x + 4 )}{2 ( x + 3 )}

s im pl i f y \frac{2 ( 256 2 - 18 3 )}{5} + 120

s im pl i f y (x^{2} + x + 1) (x^{2} - x + 1)