erweitern sin(a)(1-cos(b))+sin(b)(1-cos(a))

Lösung

erweitern

sin (a) (1 - cos (b)) + sin (b) (1 - cos (a))

sin (a) + sin (b) - sin (a + b)

Schritte zur Lösung

sin (a) (1 - cos (b)) + sin (b) (1 - cos (a))

Schreibe

sin (a) (1 - cos (b))

um:

sin (a) - cos (b) sin (a)

= sin (a) - cos (b) sin (a) + sin (b) (1 - cos (a))

Schreibe

sin (b) (1 - cos (a))

um:

sin (b) - cos (a) sin (b)

= sin (a) - cos (b) sin (a) + sin (b) - cos (a) sin (b)

Benutze die Identität der Winkelsumme:

sin (s) cos (t) + cos (s) sin (t) = sin (s + t)

- sin (s) cos (t) - cos (s) sin (t) = - sin (s + t)

= sin (a) + sin (b) - sin (a + b)

e x p an d 2 (3 + 5)

e x p an d 4 (\frac{1}{2} x + \frac{3}{2} y)

e x p an d lo g_{10} (x y z)

e x p an d (x^{2} + y^{2} + z^{2})^{4}

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