a2+b2−c2 |
2ab |
即a2+b2-c2=2ab•cosC.
再利用正弦定理可得sin2A+sin2B-sin2C=2sinAsinBcosC,
∴要证的等式成立.
(2)△ABC中,∵等式右边=4sin
A |
2 |
B |
2 |
C |
2 |
A |
2 |
B |
2 |
π−A−B |
2 |
=4sin
A |
2 |
B |
2 |
A+B |
2 |
A |
2 |
B |
2 |
A |
2 |
B |
2 |
A |
2 |
B |
2 |
=2sin2
A |
2 |
B |
2 |
=sinB+sinA-(sinBcosA+cosBsinA)=sinA+sinB-sin(A+B)
=sinA+sinB-sinC=左边,
∴要证的等式成立.