Question

prove that sin(x+y) sin(x-y)= sin x^2-sin^2​

Answer 1

Answer:

We have to prove sin(x+y)sin(x−y)=sin2x−sin2y

Solution

Let us start with RHS

sin(x+y)sin(x−y)

=(sinxcosy+cosxsiny)(sinxcosy–cosxsiny)

=(sin2xcos2y−cos2xsin2y)

=sin2x(1−sin2y)−(1−sin2x)sin2y

=sin2−sin2y

= LHS

Hence Proved

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