Math, asked by richaeldisuza, 1 year ago

Lim x tends to o xtanx/1-cosx

Answers

Answered by abhi178
3
 \lim_{n \to 0} \frac{xtanx}{1-cosx}

We know, 1 - cos2A = 2sin²A , use this concept here,
So,  \lim_{n \to 0} \frac{xtanx}{2sin^2\frac{x}{2}}

now,  \lim_{n \to 0} \frac{xtanx}{2sin^2\frac{x}{2}}\\\\= \lim_{n \to 0}\frac{tanx}{x}.\frac{x^2}{\frac{2sin^2x/2}{x^2/4}.x^2/4}\\\\ =\lim_{n \to 0}1.\frac{4x^2}{2x^2}\\\\=2
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