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## Answers

2cos(7x+5x/2).sin(7x-5x/2)/2cos(7x+5x/2).cos(7x-5x/2)

i.e; cos(12x/2).sin(2x/2)/cos(12x/2).cos(2x/2)

i.e., cos(6x).sin(x)/cos(6x).cos(x)

i.e.,sinx/cosx

i.e.,tanx=RHS

={2.cos[(7x +5x)/2].sin[(7x-5x)/2]}/{2.cos[(7x+5x)/2].cos[(7x-5x)/2]

( since,sinC-sinD=2.cos[(C+D)/2].sin[(C-D)/2]

cosC+cosD=2.cos[(C+D)/2].cos[(C-D)/2] )

=(cos3x.sinx)/(cos3x.cosx)

=sinx/cosx

=tanx

=R.H.S

=>(sin7x-sin5x)/(cos7x+cos5x)=tanx