數學M2 三角學(二) 急！！?

證明 Tan(A+B)+Tan(A－B)=(2Sin2A)/(Cos2A+Cos2B)
Sol
2P=A+B，2Q=A－B
A=P+Q，B=P－Q
[Tan(A+B)+Tan(A－B)]*(Cos2A+Cos2B)
=(Tan2P+Tan2Q)*[Cos(2P+2Q+Cos(2P－2Q))
=(Sin2P/Cos2P+Sin2Q/Cos2Q)*(2Cos2PCos2Q)
=2Sin2PCos2Q+2Sin2QCos2P
=2Sin(2P+2Q)
=2Sin2A