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if what does  `cos^(2) 3theta +cos^(2) 2theta + cos^(2) theta` equal?

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marrr | (Level 1) eNoter

Posted July 14, 2013 at 8:42 PM via web

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if what does  `cos^(2) 3theta +cos^(2) 2theta + cos^(2) theta`

equal?

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 15, 2013 at 1:39 AM (Answer #1)

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`cos(3theta)=4cos^3(theta)-3cos(theta)`

`cos^2(3theta)=(4cos^3(theta)-3cos(theta))^2`

`=16cos^6(theta)+9cos^2(theta)-24cos^4(theta)`

`cos(2theta)=2cos^2(theta)-1`

`cos^2(2theta)=(2cos^2(theta)-1)^2`

`=4cos^4(theta)+1-4cos^2(theta)`

Thus

`cos^2(3theta)+cos^2(2theta)+cos^2(theta)= `

`16cos^6(theta)+9cos^2(theta)-24cos^4(theta)+4cos^4(theta)+1-4cos^2(theta)+cos^2(theta)`

`=16cos^6(theta)-20cos^4(theta)+6cos^2(theta)+1 `

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