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Verify the identity.
cos 4x + cos 2x = 2  2 sin^2 2x  2 sin^2 x
 one year ago
 one year ago
Verify the identity. cos 4x + cos 2x = 2  2 sin^2 2x  2 sin^2 x
 one year ago
 one year ago

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TusharaBest ResponseYou've already chosen the best response.1
cos(4x)=cos(2x+2x) expand that^
 one year ago

ajprincessBest ResponseYou've already chosen the best response.2
\(\cos4x=12\sin^2 2x\) \(\cos2x=12\sin^2x\) does that help?
 one year ago

allison_Best ResponseYou've already chosen the best response.0
It did, but could you please show me how cos 4x = 1  2 sin^2 2x?
 one year ago

ajprincessBest ResponseYou've already chosen the best response.2
ya sure. \(\cos4x=\cos(2x+2x)\) \(=\cos2x\cos2x\sin2x\sin2x\) \(=\cos^2 2x\sin^2 2x\) \(=1\sin^2 2x\sin^2 2x\) \((\cos^2 2x=1\sin^2 2x)\) \(=12\sin^2 2x\)
 one year ago

allison_Best ResponseYou've already chosen the best response.0
Do you have a reference where it says cos^2 2x = 1−sin^2 2x? I think it would be useful for me since I have a formula sheet but I don't see that on here...
 one year ago

ajprincessBest ResponseYou've already chosen the best response.2
\(\cos^2x+\sin^2x=1\) Similarly \(\cos^2 2x+\sin^2 2x=1\) \(\cos^2 2x=1\sin^2 2x\)
 one year ago

allison_Best ResponseYou've already chosen the best response.0
Thank you for your time and assistance. :)
 one year ago
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