若tana=log3525,tanB=log725,则a=sina*sinB+2sin(a-B)的值属于区间?log352535是底数25是真数

Question

若tana=log35 25 ,tanB=log7 25,则a=sina*sinB+2sin(a-B)的值属于区间__________?
log35 25 35是底数 25是真数

Answer 1

a =atan(log(25)/log(35))=0.7358
B =atan(log(25)/log(7))=1.0271
sin(a)*sin(B)+2*sin(a-B)
=log(25)^2/log(35)/(log(25)^2/log(35)^2+1)^(1/2)/log(7)/(log(25)^2/log(7)^2+1)^(1/2)+2*sin(atan(log(25)/log(35))-atan(log(25)/log(7)))
=-5.0000e-032
这里给出的log是自然对数.