Step-by-step explanation:
Given:
A+B+C= π
<=> 3A+3B+3C = 3π
<=> cos(3A+3B) = - cos3C
<=> cos3A.cos3B-sin3A.sin3B = - cos3C
<=> cos3A.cos3B = sin3A.sin3B - cos3C (1)
similarly apply for the other two angles, we have:
- cos3B.cos3C = sin3B.sin3C - cos3A (2)
- cos3C.cos3A = sin3C.sin3A - cos3B (3)
Grouping three equations, (1) + (2) + (3), we have:
<=> cos3A.cos3B+cos3B.cos3C+cos3C.cos3A = sin3A.sin3B + sin3B.sin3C + sin3C.sin3A - ( cos3A + cos3B + cos3C )
= 1
Hope it can find you well.
