tan a=4,sin2a-sin^a=?
问题描述：
tan a=4,sin2a-sin^a=?
答
tana=sina/cosa=4
cosa=(1/4)sina
sin²a+cos²a=1
sin²a+[(1/4)sina]²=1
(17/16)sin²a=1
sin²a=16/17
sin(2a)-sin²a
=2sinacosa-sin²a
=2sina[(1/4)sina]-sin²a
=(-1/2)sin²a
=(-1/2)(16/17)
=-8/17
答
sin2a-sin^2a=2sinacosa-sin^2a
=(2sinacosa-sin^2a)/(sin^2a加cos^2a)
=(2tana-tan^2a)/(tan^2a加1)
tana=4
原式=(2×4-4^2)/17
=-8/17