Question #10fa9

2 Answers
Nov 14, 2017

#(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#

Nov 14, 2017

#"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"#