若tana=/13,tanb=1/2,则tan(2a+b)的值是
问题描述：
若tana=/13,tanb=1/2,则tan(2a+b)的值是
答
tan2a=2tana/(1-tan²a)
=2×1/3/[1-(1/3)²)
=(2/3)/[8/9]
=2/3×9/8
=3/4
tan(2a+b)
=(tan2a+tanb)/(1-tan2a×tanb)
=(3/4+1/2)/(1-3/4×1/2)
=(5/4)/(1-3/8)
=(5/4)/(5/8)
=5/4×8/5
=2