Question

Question #10fa9

Answer 1

`(cos(x+y)+cos(x-y))/(cosxsiny)=2coty`

Apply the identity `cos(alpha+-beta)=cosalphacosbeta+-(-sinalphasinbeta)`

`(cosxcosy-sinxsiny+cosxcosy+sinxsiny)/(cosxsiny)`
`(2cosxcosy)/(cosxsiny)`
`(2cosy)/siny`

Definitionally, this is `2coty`

Answer 2

`"see explanation"`

Explanation:

`"using the "color(blue)"addition formulae for cos"`

`•color(white)(x)cos(A+-B)=cosAcosB∓sinAsinB`

`•color(white)(x)coty=cosy/siny`

`"consider the LHS"`

`(cos(x+y)+cos(x-y))/(cosxsiny)`

`=(cosxcosycancel(-sinxsiny)+cosxcosycancel(+sinxsiny))/(cosxsiny)`

`=(2cosxcosy)/(cosxsiny)`

`=(2cancel(cosx)cosy)/(cancel(cosx)siny)`

`=2cosy/siny`

`=2coty="RHS"rArr" proved"`