Question

Помогите решить пожалуйста

Answer 1

Ответ:

Применим следующие тригонометрические формулы:

а) cos(x+y)=cosx·cosy-sinx·siny

б) cos(x-y)=cosx·cosy+sinx·siny

1) По формуле а):

cos3α·cosα-sinα·sin3α=cos(3α+α)=cos4α

2) По формуле б):

cos5β·cos2β+sin5β·sin2β=cos(5β-2β)=cos3β

3) По формуле а):

cos(π/7+α)·cos(5π/14-α)-sin(π/7+α)·sin(5π/14-α)=

=cos(π/7+α+5π/14-α)=cos(2π/14+5π/14)=cos(7π/14)=cos(π/2)=0

2) По формуле б):

cos(7π/5+α)·cos(2π/5+α)+sin(7π/5+α)·sin(2π/5+α)=

=cos((7π/5+α)-(2π/5+α))=cos(7π/5+α-2π/5-α)=cos(5π/5)=cos(π)= -1