Asked by stacey graham
verify the identity:
sin(x+y)-sin(x-y)=2cosx siny
sin(x+y)-sin(x-y)=2cosx siny
Answers
Answered by
Ashish
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.
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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