JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If \(\dfrac{\pi}{4} + \displaystyle\sum_{p=1}^{11} \tan^{-1}\left(\dfrac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha\), then \(\tan\alpha\) is equal to __________.
- A 20.48
- B 2048
- C 2.048
- D 204.8
Answer & Solution
Correct Answer
(B) 2048
Step-by-step Solution
Detailed explanation
The general term of the given series is \(T_p = \tan^{-1}\left(\dfrac{2^{p-1}}{1 + 2^{2p-1}}\right)\). This can be rewritten by expressing the numerator and denominator in terms of \(2^p\) and \(2^{p-1}\):…
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