Question

lim x tends to 0 :cos2x-1/cosx-1

Answer 1

answer is 4.

we have to find $\displaystyle\lim_{x\to 0}\frac{cos2x-1}{cosx-1}$

we know, cos2θ = 2cos²θ - 1

so,cos2x = 2cos²x - 1

⇒cos2x - 1 = 2cos²x - 2

= 2(cos²x - 1)

= 2(cosx - 1)(cosx + 1)

now, $\displaystyle\lim_{x\to 0}\frac{cos2x-1}{cosx-1}$ = $\displaystyle\lim_{x\to 0}\frac{2(cosx-1)(cosx+1)}{(cosx-1)}$

= $\displaystyle\lim_{x\to 0}2(cosx+1)$

putting, x = 0

= 2(cos0 + 1) = 2 (1 + 1)

= 4

hence, answer is 4.

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Answer 2

Step-by-step explanation:

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