erweitern 2(cos(5x)+cos(3x))(sin(3x)-sin(x))

Lösung

erweitern

2 (cos (5 x) + cos (3 x)) (sin (3 x) - sin (x))

sin (2 \cdot 3 x) + 2 cos (5 x) sin (3 x) - 2 cos (3 x) sin (x) - 2 cos (5 x) sin (x)

Schritte zur Lösung

2 (cos (5 x) + cos (3 x)) (sin (3 x) - sin (x))

Schreibe

2 (cos (5 x) + cos (3 x)) (sin (3 x) - sin (x))

um:

2 (cos (5 x) sin (3 x) - cos (5 x) sin (x) + cos (3 x) sin (3 x) - cos (3 x) sin (x))

= 2 (cos (5 x) sin (3 x) - cos (5 x) sin (x) + cos (3 x) sin (3 x) - cos (3 x) sin (x))

Setze Klammern

= 2 cos (5 x) sin (3 x) + 2 (- cos (5 x) sin (x)) + 2 cos (3 x) sin (3 x) + 2 (- cos (3 x) sin (x))

Vereinfache

2 cos (5 x) sin (3 x) + 2 (- cos (5 x) sin (x)) + 2 cos (3 x) sin (3 x) + 2 (- cos (3 x) sin (x)) : sin (2 \cdot 3 x) + 2 cos (5 x) sin (3 x) - 2 cos (3 x) sin (x) - 2 cos (5 x) sin (x)

= sin (2 \cdot 3 x) + 2 cos (5 x) sin (3 x) - 2 cos (3 x) sin (x) - 2 cos (5 x) sin (x)

s im pl i f y s (1 + \frac{s}{3}) (1 + \frac{s}{20})

e x p an d \frac{( 6 x ^{2} - 3 ) ^{4}}{( 2 x ^{3} + 8 ) ^{5}}

e x p an d 3 (3 - 1)

e x p an d \frac{2}{( 1 + x ) ^{3}}

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