1 向量a=(sinX;3/2)=-3/2(-2/3sinX,-1),向量b=(cosX,-1)
a//b
-2/3sinx=cosx
tanx=-3/2
2cos^2x—sin2x=2(cosx)^2-sin2x=cos2x+1+sin2x
=[1+(tanX)^2]/[1-(tanx)^2]+1+2tanx/[1-tanX)^2]
=[1+(-3/2)^2]/[1-(-3/2)^2]+1+2(-3/2)/[1-(-3/2)^2]=4/5
2 F(x)=(a+b)b在〔－π／2,0
a+b=([sinx-3/2cosx],1/2)
|a+b|=[(sinx-1.5cosx)^2+1/4]^0.5
k1=(1/2)/(sinx-3/2cosx)=1/(2sinx-3cosx)
|b|=[(cosx)^2+1]^0.5
k2=-1/cosX
tanN=|(k2-k1)/(1+k1k2)|=2/(sinx+3cosx)
cosN=
F(x)=(a+b)b=|a+b||b|cosN=