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If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^...

If `x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2)` is `n^2x` (b) `-n^2x` (c) `-n x` (d) `n x`

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Given,`x=acos(nt)−bsin(nt)`
⇒`dx/dt​=−nasin(nt)−nbcos(nt)`
⇒`d^2x/dt^2​=−n^2a(cos(nt))+n^2bcos(nt)`
=`−n^2(acosnt−bsinnt)=−n^2x`
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