Question

8cosB*cos2B*cos4B

cos3B*cos5B*cos8B

Answer 1

Решение:

Преобразование произведения тригонометрических функций в сумму

1) 8 cosβ · cos2β · cos4β =  8 cosβ · 0,5 (cos6β + cos2β) =

= 4 cosβ · cos6β + 4 cosβ · cos2β =

= 4 · 0.5 (cos7β + cos5β) +  4 · 0.5 (cos3β + cosβ) =

= 2(cos7β + cos5β + cos3β + cosβ)

2) cos3β · cos5β · cos8β = cos3β · 0.5( cos13β + cos3β)

= 0.5 (cos3β · cos13β - cos3β · cos3β) =

= 0.25 (cos16β + cos 10β + cos6β + cos 0) =

= 0.25 (cos16β + cos 10β + cos6β + 1)