Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

P Lim X → 0 Sin 3 X − Sin X Sin X - Mathematics

\[\lim_{x \to 0} \frac{\sin 3x - \sin x}{\sin x}\] 

Advertisement Remove all ads

Solution

\[\lim_{x \to 0} \left[ \frac{\sin 3x - \sin x}{\sin x} \right]\]

\[= \lim_{x \to 0} \left[ \frac{2 \cos\left( \frac{3x + x}{2} \right) \sin\left( \frac{3x - x}{2} \right)}{\sin x} \right] \left[ \because \sin C - \sin D = 2\cos\left( \frac{C + D}{2} \right)\sin\left( \frac{C - D}{2} \right) \right]\]
\[ = \lim_{x \to 0} \left[ \frac{2 \cos2x . \sin x}{\sin x} \right]\]
\[ = 2\cos0\]
\[ = 2\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.7 | Q 22 | Page 50
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×