Докажите тождество: sina + cosa - sin(a - π/6) + cos(a - π/6) = √6cos(a - π/12)

Question

Докажите тождество:
sina + cosa - sin(a - π/6) + cos(a - π/6) = √6cos(a - π/12)

Answer 1

2sinπ/12cos(a-π/12)+2cosπ/12cos(a-π/12)=
=2cos(a-π/12)*(sinπ/12+cosπ/12)=2cos(a-π/12)(sinπ/12+sin5π/12)=
=2cos(a-π/12)*2sinπ/4cosπ/6=4*√2/2*√3/2cos(a-π/12)=√6cos(a-π/12)