Question

在三角形ABC中,abc成等比数列,cos=0.75 求1/tanA +1/tanC的值

Answer 1

a,b,c成等比数列,所以a*c=b^2

根据正弦定理,a/sinA=b/sinB=c/sinC

所以sinA=a/b*sinB,sinC=c/b*sinC

1/tanA +1/tanC=cosA/sinA+cosC/sinC

=(cosA*sinC+sinA*cosC)/sinA*sinC

=sin(A+C)/[(a/b*sinB)*(c/b*sinC)]

=sinB/[(a/b*sinB)*(c/b*sinC)]

=1/sinB

=4/(根号7）