Question

tan70°- tan10°- 根号3tan70° x tan10°的值 已知sin(x-B/2)=4/5,cos(x/

Answer 1

（一）√3=tan60º=tan(70º-10º)=(tan70-tan10)/(1+tan70tan10).===>tan70-tan10=(1+tan70tan10)√3=(√3)+(√3)tan70tan10).===>tan70-tan10-(√3)tan70tan10=√3.(二）sin(x-B/2)=4/5.cos(x-B/2)=-3/5.cos(x/2-B)=-12/13,sin(x/2-B)=-5/13.sin[(x+B)/2]=sin[(x-B/2)-(x/2-B)]=sin(x-B/2)cos(x/2-B)-cos(x-B/2)sin(x/2-B)=-63/65.cos[(x+B)/2]=cos[(x-B/2)-(x/2-B)]=cos(x-B/2)cos(x/2-B)+sin(x-B/2)sin(x/2-B)=56/65.∴tan[(x+B)/2]=-9/8.