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

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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 `