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Coefficient of x3 in the expansion of tan x is
- a)1/3
- b)2/15
- c)1/2
- d)1/4
Correct answer is option 'A'. Can you explain this answer?
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Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Corr...
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Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Corr...
Understanding the Expansion of tan x
To find the coefficient of \( x^3 \) in the expansion of \( \tan x \), we can utilize the Taylor series expansion around \( x = 0 \).
Taylor Series for tan x
The Taylor series for \( \tan x \) is given by:
\[
\tan x = x + \frac{x^3}{3} + \frac{2x^5}{15} + \frac{17x^7}{315} + \cdots
\]
From this expansion, we can observe the terms involving \( x^3 \).
Identifying the Coefficient of x^3
- The term involving \( x^3 \) is \( \frac{x^3}{3} \).
- Therefore, the coefficient of \( x^3 \) in the expansion of \( \tan x \) is \( \frac{1}{3} \).
Conclusion
Thus, the correct answer for the coefficient of \( x^3 \) in the expansion of \( \tan x \) is:
- Option (a) \( \frac{1}{3} \).
This concludes the analysis, confirming that the expansion aligns with the Taylor series, leading us to the desired coefficient.
To find the coefficient of \( x^3 \) in the expansion of \( \tan x \), we can utilize the Taylor series expansion around \( x = 0 \).
Taylor Series for tan x
The Taylor series for \( \tan x \) is given by:
\[
\tan x = x + \frac{x^3}{3} + \frac{2x^5}{15} + \frac{17x^7}{315} + \cdots
\]
From this expansion, we can observe the terms involving \( x^3 \).
Identifying the Coefficient of x^3
- The term involving \( x^3 \) is \( \frac{x^3}{3} \).
- Therefore, the coefficient of \( x^3 \) in the expansion of \( \tan x \) is \( \frac{1}{3} \).
Conclusion
Thus, the correct answer for the coefficient of \( x^3 \) in the expansion of \( \tan x \) is:
- Option (a) \( \frac{1}{3} \).
This concludes the analysis, confirming that the expansion aligns with the Taylor series, leading us to the desired coefficient.
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Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Correct answer is option 'A'. Can you explain this answer?.
Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Coefficient ofx3 in the expansion of tan x isa)1/3b)2/15c)1/2d)1/4Correct answer is option 'A'. Can you explain this answer?.
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