If &radic;2 cos x = cosy + cos 3 y and &radic;2 sinx = siny &minus; sin 3 y then determine the value of sin(x &minus; y)

Nirabhra Agrawal Grade: 12

        

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

7 years ago

Answers : (1)

AKASH GOYAL AskiitiansExpert-IITD

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
AskiitiansExpert-IITD
 
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