MCQ
$\lim_{x \rightarrow 0}\left(cosec^3xcotx-2cot^3xcosecx+\frac{cot^4x}{secx}\right)=........$
- A8
- ✓1
- C4
- D3
$=\lim_{x \rightarrow 0}\frac{cosx}{sin^4x}-\frac{2cos^3x}{sin^4x}+\frac{cos^5x}{sin^4x}$
$=\lim_{x \rightarrow 0}\frac{cosx-2cos^3x+cos^5x}{sin^4x}$
$=\lim_{x \rightarrow 0}\frac{cosx(1-2cos^2x+cos^4x)}{sin^4x}$
$=\lim_{x \rightarrow 0}\frac{cosx(1-cos^2x)^2}{(1-cos^2x)^2}=x.$
$=\lim_{x \rightarrow 0}=\cos u$
$=1$
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