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Show that cos^2theta+cos^2theta(alpha+th...

Show that `cos^2theta+cos^2theta(alpha+theta)-2cosalphacostheta"cos"(alpha+theta)` is independent of `thetadot`

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`cos^(2)theta+cos^(2)(alpha+theta)-2cosalpha cos theta cos (alpha+theta)`
`=cos^(2)theta+cos(alpha+theta)[cos(alpha+theta)-2cos alpha cos theta]`
`=cos^(2)theta+cos(alpha+theta)`
`[cos alpha cos theta-sin alpha sin theta-2cos alpha cos theta]`
`cos^(2)theta-cos(alpha+theta)(cos alpha cos theta+sin alpha sin theta)`
`=cos^(@)theta-cos(alpha+beta)cos(alpha-theta)`
`=cos^(2)theta-[cos^(2)alpha-sin^(2)theta]=cos^(2)theta+sin^(2)theta-cos^(2)alpha`
`=1-cos^(2)alpha`, which is independent of `theta`.
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