Question

1
2 W 2.082
. Să se transforme în produs:
c) sin a + sin b+sin (a - b);
d) cos a - cos b + sin (a + b).
Dau coronița ​

Answer 1

Răspuns:

Explicație pas cu pas:

$c)~sin\alpha +sin\beta +sin(\alpha -\beta)=2sin\frac{\alpha+\beta }{2}cos \frac{\alpha-\beta }{2}+sin(2*\frac{\alpha-\beta }{2})=\\=2sin\frac{\alpha+\beta }{2}cos \frac{\alpha-\beta }{2}+2sin\frac{\alpha-\beta }{2}cos \frac{\alpha-\beta }{2}=2cos\frac{\alpha-\beta}{2}*( sin\frac{\alpha+\beta }{2}+sin\frac{\alpha-\beta }{2}).\\d)~~cos\alpha-cos\beta +sin(\alpha +\beta )=-2sin\frac{\alpha+\beta }{2}sin \frac{\alpha-\beta }{2}+sin(2*\frac{\alpha+\beta }{2})=$

$=-2sin\frac{\alpha+\beta }{2}sin\frac{\alpha-\beta}{2}+2sin\frac{\alpha+\beta }{2}cos\frac{\alpha+\beta}{2} =2sin\frac{\alpha+\beta}{2}*(-sin\frac{\alpha-\beta}{2}+cos\frac{\alpha+\beta}{2})$