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