`f)` Áp dụng:
`cos(a-b)=cosacosb+sinasinb`
`cos2a=1-2sin^2a`
_____
Ta có:
`VT=sin(x+y)sin(x-y)+cos(x+y)cos(x-y)`
`=cos[(x+y)-(x-y)]=cos(x+y-x+y)=cos2y`
`=1-2sin^2y=VP`
Vậy: `sin(x+y)sin(x-y)+cos(x+y)cos(x-y)=1-2sin^2y`
$\\$
`g)` $VP=$
`\qquad {2sin(x+y)}/{cos(x+y)+cos(x-y)}`
`={2(sinxcosy+cosxsiny)}/{cosxcosy-sinxsiny+cosxcosy+sinxsiny}`
`={2(sinxcosy+cosxsiny)}/{2cosxcosy}`
`={sinxcosy}/{cosxcosy}+{cosxsiny}/{cosxcosy}`
`={sinx}/{cosx}+{siny}/{cosy}`
`=tanx+tany=VT`
Vậy: `tanx+tany={2sin(x+y)}/{cos(x+y)+cos(x-y)}`
