COMEDK · Maths · 16. Limits
\(\text { The value of } \lim _\limits{x \rightarrow 0} \dfrac{\sin (a+x)-\sin (a-x)}{x} \text { is }\)
- A 1
- B \(2 \cos a\)
- C 0
- D \(2 \sin a\)
Answer & Solution
Correct Answer
(B) \(2 \cos a\)
Step-by-step Solution
Detailed explanation
The given limit is \(L = \lim_{x \to 0} \dfrac{\sin(a+x) - \sin(a-x)}{x}\). Using the trigonometric identity \(\sin C - \sin D = 2 \cos \left( \dfrac{C+D}{2} \right) \sin \left( \dfrac{C-D}{2} \right)\), we set \(C = a+x\) and \(D = a-x\). Then…
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