三角恆等式

條題目沒有n﹐用不到數學歸納法(mathematical induction)
1-4sin(3A/2)sin(3B/2)sin(3C/2)
=1-2sin(3C/2)[cos3(A-B)/2 -cos3(A+B)/2]
=1-[sin3(A-B+C)/2 -sin3(A-B-C)/2] +[sin3(A+B+C)/2 -sin3(A+B-C)/2]
=-sin3(A-B+C)/2 +sin3(A-B-C)/2 - sin3(A+B-C)/2
=-sin3(180-B-B)/2 +sin3(A+A-180)/2 -sin3(180-C-C)/2
=-sin(270-3B) -sin(270-3A) -sin(270-3C)
=cos3A+cos3B+cos3C
公式
sum to product formula:

1. 2sinAcosB=sin(A+B)+sin(A-B)
2. 2cosAcosB=cos(A+B)+cos(A-B)
3. 2sinAsinB=cos(A-B)-cos(A+B)

product to sum formula:

4.sinA+sinB=2[sin(A+B)/2][cos(A-B)/2]
5.cosA+cosB=2[cos(A+B)/2][cos(A-B)/2]
6.cosA-cosB=-2[sin(A+B)/2][sin(A-B)/2]