Sin6x cosx + cos6x sin= 1/2 Как решить?

Question

Sin6x cosx + cos6x sin= 1/2
Как решить?

Answer 1

Sin(6x + x) = 1/2
sin 7x = 1/2

7x = arcsin1/2 + 2pik
7x = pi/6 + 2pik
x = pi/42 + (2pik)/7, k ∈Z

7x = pi - arcsin1/2 + 2pik
7x = pi - pi/6 + 2pik
7x = 5pi/6  + 2pik
x = (5pi)/42 + (2pik)/7, k ∈Z

Comments

Спасибо большое