Question

Докажите тождества

1. cos3a*cos6a-cos4a*cos7a=sin10a*sina
2. на картинке

Answer 1

Answer:

Cos9A + cos3A + cos7A + cos5A

{ 2 cos ( 9A + 3A / 2 ) cos ( 9A - 3A / 2 ) } + { 2 cos ( 7A+ 5A / 2) cos ( 7A - 5A / 2 ) }

( 2 cos6A cos3A ) + ( 2 cos6A cosA )

2 cos6A ( cos3A + cosA )

2 cos6A { 2 cos ( 3A + A / 2) cos ( 3A - A / 2 ) }

2 cos6A ( 2 cos2A cosA )

4 cosA cos2A cos6A = RHS