数学多可爱,锐角A满足logsinA(tanA+cotA)=-4/3,则logtanAcosA的值为?

Question

数学多可爱,
锐角A满足logsinA(tanA+cotA)=-4/3,则logtanAcosA的值为?

Answer 1

logsina(tana+cota)
= logsina(sina/cosa+cosa/sina)
= logsina(1/sinacosa)
=-1*logsina(sinacosa)
=-logsinasina-Logsinacosa
=-1-logsinacosa
=-4/3
所以logsinacosa=1/3
Logtanacosa
= Logsinacosa/ Logsina(sina/cosa)
= Logsinacosa/ (Logsinasina-- Logsinacosa)
=(1/3)/(1—1/3)
=1/2
所以Logtanacosa=1/2