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If √2 cos x = cosy + cos3y and √2 sinx = siny − sin3y then determine the value of  sin(x − y)
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7 years ago

419 Points
```										Dear Nirabhra
sin(x-y)=sinx*cosy-cosx*siny
=1/√2 [(siny-sin3y)*cosy - (cosy + cos3y)*siny]
=1/√2 [siny(1-sin2y)*cosy - (cosy + cos3y)*siny]
=1/√2 [siny*cos2y*cosy - (cosy + cos3y)*siny]
=1/√2 [siny*cos3y - (cosy + cos3y)*siny]
take siny common
=1/√2 * siny [cos3y - cosy - cos3y]
= - siny*cosy/√2
= -sin2y/2√2
All the best.
AKASH GOYAL

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7 years ago
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