Question 1189411


{{{tan(x) + tan(x)cos(2x)=sin(2x)}}}

manipulate left side

{{{tan(x)(1 + cos(2x)) }}}...........use Double-Angle Identities {{{cos(2x)=2cos ^2(x)-1}}} and identity {{{tan(x)=sin(x)/cos(x)}}}

={{{(sin(x)/cos(x))(1+2cos ^2(x)-1) }}}

={{{(sin(x)/cos(x))(2cos ^2(x)) }}}..........simplify

={{{2sin(x)cos (x)}}}....................use Double-Angle Identities {{{sin(2x)= 2sin(x)cos (x)}}}

={{{sin(2x)}}}-> proven