1、cosx-cosy=1/2 ,sinx-siny=-1/3
分别两边平方
(cosx)^2-2cosxcosy+(cosy)^2=1/4
(sinx)^2-2sinxsiny+(siny)^2=1/9
相加
且(cosx)^2+(sinx)^2=1 (cosy)^2+(siny)^2=1
2-2(cosxcosy+sinxsiny)=1/4+1/9=13/36
cos(x-y)=cosxcosy+sinxsiny
=(2-13/36)/2
=59/72
2、sinπ/14 sin3π/14 sin5π/14
= cos6π/14 cos4π/14 cos2π/14
=cosπ/7 cos2π/7 cos3π/7……(1)
因2sinθcosθ=sin2θ
又sin3π/7=sin4π/7sin6π/7=sinπ/7
所 (1)*sinπ/7= sinπ/7 cosπ/7 cos2π/7 cos3π/7
=1/2 sin2π/7 cos2π/7 cos3π/7
=1/4 sin4π/7 cos3π/7
=1/4 sin3π/7 cos3π/7
=1/8 sin6π/7
=1/8 sinπ/7
而(1)*sinπ/7=1/8 sinπ/7
所(1)式=1/8
3、tan60=tan(20+40)=(tan20+tan40)/(1-tan20tan40)
tan20+tan40=tan60(1-tan20tan40)
(tan20+tan40+tan120)/tan20*tan40
=[tan60(1-tan20tan40)-tan60]/(tan20*tan40)
=-(tan60tan20tan40)/(tan20*tan40)
=-tan60
=-√3
终于做完了,手好酸啊