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anonymous
 one year ago
Verify the identity.
cos(4u) = cos^2(2u)  sin^2(2u)
anonymous
 one year ago
Verify the identity. cos(4u) = cos^2(2u)  sin^2(2u)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\cos \left( 4u\right) = \cos ^{2}\left( 2u \right)  \sin ^{2}\left( 2u \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@arindameducationusc

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Do you know Cos2theta= cos^2thetasin^2theta?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, double angle identity

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: we can rewrite the left side as below: \[\Large \cos \left( {4u} \right) = \cos \left( {2u + 2u} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now you can apply the formula of addition for cosine function

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2\[\Large \cos \left( {x + y} \right) = \cos x\cos y  \sin x\sin y\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cos ( 2u + 2u ) = cos (2u) cos (2u)  sin (2u) sin (2u) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do i do from there?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2it is simple, since: \[\Large \cos \left( {2u} \right)\cos \left( {2u} \right) = {\left( {\cos \left( {2u} \right)} \right)^2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2similarly for sin(2u)*sin(2u)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin(2u) sin(2u) = (sin(2u))^2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so since im trying to verify this identity, what else do i do to get the answer to look like cos(4u) = cos(4u) ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2since we have proven that left side is equal to right side, then we are done here

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so is the final answer cos ( 2u + 2u ) = cos (2u) cos (2u)  sin (2u) sin (2u) or cos(2u) cos(2u) = (cos(2u))^2 ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the answer is the entire procedure which shows how to get the right side, starting from left side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahhhhhh, i see, i see. thank you soooooo much for your help!
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