Question

已知sin(a+b)=1/2,sin(a-b)=1/3.(1)求证：sinaco *** =5cosasinb(2)求证：ta？

Answer 1

（1）因为
sin（a-b）=sin(a)*cos(b)-cos(a)*sin(b)=1/3
sin（a+b）=sin(a)*cos(b)+cos(a)*sin(b)=1/2
3sin(a)*cos(b)-3cos(a)*sin(b)=1
2sin(a)*cos(b)+2cos(a)*sin(b)=1
3sin(a)*cos(b)-3cos(a)*sin(b)=2sin(a)*cos(b)+2cos(a)*sin(b)
所以解得sinaco *** =5cosasinb
（2）因为tana=5tanb
原试可以换成sina/cosa=5sinb/co ***
对掉一下位置,就同证明第一题一样啦,10,已知sin(a+b)=1/2,sin(a-b)=1/3.(1)求证：sinaco *** =5cosasinb(2)求证：tana=5tanb