If `x=f(t)cost-f^(prime)(t)sint` and `y=f(t)sint+f^(prime)(t)cost ,` then `((dx)/(dt))^2+((dy)/(dt))^2=` (a)`f(t)-f^(primeprime)(t)` (b) `{f(t)-f^(primeprime)(t)}^2` (c) `{f(t)+f^(primeprime)(t)}^2` (d) none of these

Explanation

`x=f(t) cos t-f^{prime}(t) sin t`
`
`y=f(t) sin t+f^{prime}(t) cos `t

`frac{d x}{d t}=f^{prime}(t) cos t-f(t) sin t-f^{prime prime}(t) sin t-f^{prime}(t) cos t`
`
=-f(t) sin t-f^{prime prime}(t) sin t`
`
=-sin t[f(t)+f^{prime prime}(t)] `
`
frac{d x}{d t}=f^{prime}(t) sin t-f(t) cos t-f^{prime prime}(t) sin t-f^{prime}(t) sin t`
`
=-f(t) cos t-f^{prime prime}(t) cos t`
`
=cos [F(t)+f^{prime prime}(t)] `
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