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

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Grade 12Trigonometry

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

Nirabhra Agrawal

15 Years agoGrade 12

1 Answer

AKASH GOYAL AskiitiansExpert-IITD

15 Years ago

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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