1) sin 2π + sin π = 2 sin 2π+π cos 2π-π = 2 sin 3π cos π
5 5 5*2 5*2 10 10
2) cos 11π + cos 3π = cos11π + cos 9π = 2 cos 11π+9π cos 11π-9π =
12 4 12 12 12*2 12*2
=2 cos 20π cos 2π = 2 cos 5π cos π
24 24 6 12
3) cos(π/3 - α) + cosα =2 cos(π/3 - α+α) cos (π/3 -α-α) =
2 2
=2 cos π cos(π - α) = 2 *√3 cos(π - α) = √3 cos(π - α)
6 6 2 6 6
=√3 (cosπ cosα + sinπ sinα) =√3 (√3 cosα + sinα)
6 6 2 2
4) sin(π/6 +α) - sin(π/6 -α) = 2 sin (π/6 +α-π/6+α) cos(π/6 +α+π/6-α) =
2 2
=2 sinα cosπ/6 = 2 * √3 sinα =√3 sinα
2
5) sin π/6 - sin π/9 = sin 3π/18 - sin 2π/18 =
= 2 sin (3π-2π) cos (3π+2π) = 2 sin π cos 5π
18*2 18*2 36 36
6) sinα - sin (α +π/3) = 2 sin (α-α-π/3) cos (α+α+π/3) =
2 2
=2 sin (-π/6) cos(α+π/6) = -2 * (1/2) cos(α + π/6) =
=-cos(α+π/6) = -(cosα cosπ/6 - sinα sin π/6) =
= -(√3 cosα - (1/2) sinα) =1 (sinα - √3 cosα)
2 2