Question

verify the identity:
sin(x+y)-sin(x-y)=2cosx siny
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.

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