Question

1. Найдите значения выражений. а) sin(133°)cos(73°)−cos(133°)sin(73°)sin⁡(133°)cos(73°)−cos(133°)sin(73°). б) cos(π14)cos(19π28)−sin(π14)sin(19π28)cos⁡(π14)cos(19π28)−sin(π14)sin(19π28).

Answer 1

а)     $sin133^ocos73^o-cos133^osin73^o=$

     $=sin(133^o-73^o)=sin60^o=\frac{\sqrt{3} }{2}$

Ответ:  $\frac{\sqrt{3} }{2}$

б)     $cos(\frac{\pi }{14} )cos(\frac{19\pi }{28} )-sin(\frac{\pi }{14} )sin(\frac{19\pi }{28} )=$

   $=cos(\frac{\pi }{14} +\frac{19\pi }{28} )=cos{\frac{21\pi }{28} =cos\frac{3\pi }{4} =-\frac{\sqrt{2} }{2}$

Ответ:   $-\frac{\sqrt{2} }{2}$

Answer 2

а) sin(133°)cos(73°)−cos(133°)sin(73°)=sin(133°-73°)=sin60°=(√3)/2

б) cos(π/14)cos(19π/28)−sin(π/14)sin(19π/28)=cos⁡((π/14)+(19π28))=cos(21π/28)=

=cos(3π/4)=-√2/2