已知向量a(1,sinx),b(sinx^2x,cosx)函数f(x)=ab,x属于[0,90°]

题目

已知向量a(1,sinx),b(sinx^2x,cosx)函数f(x)=ab,x属于[0,90°]
求f(α)=3/4 求sin2α

答案

f(x)=ab
=sin^2x+sinxcosx
=0.5-0.5cos2x+0.5sin2x
0.25/0.5=1/2=sin2x-cos2x
=(2tana-1)/1+tan^2a)
1+tan^2a=4tana-2
tan^2a-4tana+3=0
(tana-1)(tana-3)=0
tana=1,and tana=3
sin2a=2tana/(1+tan^2a)
①
sin2a=2/(1+1)=1
②
sin2a=6/(1+9)=3/5