Question

求证：sina+sinb/(cosa+cosb)=tan[(a+b)/2]

Answer 1

设cosA+cosB=t，
则(sinA+sinB)/(cosA+cosB)
=[2sin(A+B)/2.cos(A-B)/2]/[2cos(A+B)/2.cos(A-B)/2]
=tan(A+B)/2

追问

若sina+sinb=l/4，cosa+cosb=1/3,求tan(a十b)=?

追答

再开一题吧送好评

sina+sinb)(cosa+cosb)=1/12，sinacosa+sinbcosb+sin(a+b)=1/12，sin(a+b)cos(a-b)+sin(a+b)=1/12；(sina+sinb)²+(cosa+cosb)²=1/16+1/9，2cos(a-b)+2=25/16*9，cos(a-b)=-263/288，代入sin(a+b)cos(a-b)+sin(a+b)=1/12，得：sin(a+b)=24/25；
(cosa+cosb)²-(sina+sinb)²=1/9-1/16，2cos(a+b)+2cos(a+b)cos(a-b)=7/16*9，得：cos(a+b)=7/25，则tan(a+b)=24/7