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Question
Evaluate the following limit.
`lim_(x -> 0) (cos 2x -1)/(cos x - 1)`
Solution
`lim_(x → 0) (cos 2x - 1)/(cos x - 1)`
= `lim_(x → 0) (1 - 2 sin^2 x - 1)/(cosx - 1)`
= `lim_(x → 0) (2sin^2 x)/(1 - cosx)`
= `lim_(x → 0) (2(1 - cosx)(1 + cosx))/(1 - cosx)`
= `lim_(x → 0) 2(1 + cosx)`
= 2(1 + cos 0)
= 2 × 2
= 4
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