verify the identity:

Question

sin(x+y)-sin(x-y)=2cosx siny

Answer 1

hey stacey..

we know that,
sin(x+y)= sinx cosy + cosx siny
and
sin(x-y)= sinx cosy - cosx siny

so,

sin(x+y)-sin(x-y)

= {sinx cosy + cosx siny} - {sinx cosy - cosx siny}

= sinx cosy + cosx siny - sinx cosy + cosx siny

=cosx siny + cosx siny

=2cosx siny

hence verified.