Question 1170381


{{{sin(0.6x)-sin(0.4x)}}}

let {{{u=0.1x}}}

then we have

{{{sin(6u)-sin(4u)}}}

use the following identity : {{{sin(s )- sin(t )=2cos((s+t)/2)sin((s-t)/2) }}}where {{{s=6u}}} and{{{ t=4u}}}

{{{sin(6u )- sin(4u )=2cos((6u+4u)/2)sin((6u-4u)/2)}}}

{{{sin(6u )- sin(4u )=2cos(10u/2)sin(2u/2)}}}

{{{sin(6u )- sin(4u )=2cos(5u)sin(u)}}} ............since {{{u=0.1x}}}

{{{sin(6*0.1x )- sin(4*0.1x )=2cos(5*0.1x)sin(0.1x)}}}

{{{sin(0.6x )- sin(0.4x )=2cos(0.5x)sin(0.1x)}}}


so, answer is

a. {{{2cos(0.5x)sin(0.1x)}}}