Question

Evaluate the following limit :-
$\lim_{ \bf \: x \to \: 0} \dfrac{ \cos 2x - 1}{ \cos \: x - 1}$
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Answer 1

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Answer 2

ANSWER:-

4

QUESTION:-

$\bf\; {\lim_{x \to 0}}=\frac{cos\;2x-1}{cos\;x-1}$

EXPLANATION:-

ON SIMPLIFYING:-

cos 2x -1=1-2 sin²x-1=

cos2x-1=-2sin²x

NOW,

-2sin²x=-2(1- cosx)(1+cosx)

2(cosx+1)(cosx-1)

NOW,

$\bf\; \lim_{x \to 0} \frac{2(c0sx+1)(cosx-1)}{(cosx-1)}$

2(cos 0+1)

⇒4