Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(cos2x-1)/(cos x-1)`

Text Solution

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`lim_(x->0)(cos2x-1)/(cos x-1)`
As `cos2x−1=1−2sin^2x−1=−2sin^2x`
`−2sin^2x=−2(1−cosx)(1+cosx)`
Then
`=lim_(x->0)(2(cosx+1)(cos x-1))/(cos x-1)`
`=2(cos 0 +1)`
`=4`

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