Răspuns:
Explicație pas cu pas:
[tex]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})=\\[/tex]
[tex]=-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})[/tex]
