在△ABC中,若sinA=2cosBcosC,则tanB+tanC=_.
问题描述:
在△ABC中,若sinA=2cosBcosC,则tanB+tanC=______.
答
tanB+tanC=
+sinB cosB
=sinC cosC
=sinBcosC+cosBsinC cosBcosC
=sin(B+C) cosBcosC
=sin(π−A) cosBcosC
=2sinA cosBcosC
故答案为:2