Question

Записати у виглядi добутку:
а) sin3α+sinα
б) cos46°-cos74°
в) cos 11π/12 + cos 3π/4

Answer 1

а) sin3α+sinα=$2sin\frac{3\alpha +\alpha }{2} * cos\frac{3\alpha -\alpha }{2}$ =2sin2α*cosα

б) cos46°- cos74° =$- 2sin\frac{3\alpha +\alpha }{2} * sin\frac{3\alpha -\alpha }{2}$ = -2sin2α*sinα

в) cos 11π/12 + cos 3π/4 =$2cos\frac{\frac{11\pi }{12} +\frac{3\pi }{4} }{2} * cos\frac{\frac{11\pi }{12} +\frac{3\pi }{4} }{2}$ =

=2cos(20π/24)*cos(π/12)=2cos(5π/6)*cos(π/12)