Представте в виде произведения: 1)sin 12°+sin 20° 2)sin 52°-sin 32° 3)cos π/10- cos...

Question

Представте в виде произведения:

1)sin 12°+sin 20°

2)sin 52°-sin 32°

3)cos π/10- cos π/20

4)sin π/6 - sin π/9

5)sin α-sin(α+π/3)

6)cos(π/4 + α) - cos(π/4-α)

Answer 1

Формулы сложения применить надо.

1)sin12+sin20=2 sin16 cos4

2)sin52-sin32=2sin10 cos42

3)cosπ/10-cos/20= -2sinπ/40 sin 3π/40

4)  sinπ/6-sinπ/9=2 sinπ/36 cos5π/36

5)sinα-sin(α+π/3)=2 sin(-π/6) cos(α+π/6)= -2sinπ/6 c0s(α+π/6)=-2*1/2* cos(α+π/6)=

 = -cos(α+π/6)

6)cos(π/4+α)-cos(π/4-α)= -2 sinπ/4 sinα