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JEE Main 202125 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Evening Shift
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2021 · 25 February · Evening Shift · Mathematics · Inverse Trigonometric Functions

cosec [2 ^ - 1 (5) + ^ - 1 ((4)/(5))] is equal to:

coseccosec\left[2\cot^{- 1}\left(5\right) + \cos^{- 1}\left(\dfrac{4}{5}\right)\right] is equal to:

Options

  1. A6556\dfrac{65}{56}
  2. B7556\dfrac{75}{56}
  3. C6533\dfrac{65}{33}
  4. D5633\dfrac{56}{33}

Correct answer

A. 6556\dfrac{65}{56}

Step-by-step solution

Given, cosec[2tan⁡−1(15)+tan⁡−1(34)]cosec \left[2\tan^{- 1}\left(\dfrac{1}{5}\right) + \tan^{- 1}\left(\dfrac{3}{4}\right)\right]

=cosec[tan⁡−1(2×(15)1−(125))+tan⁡−1(34)]= cosec \left[\tan^{- 1}\left(\dfrac{2 \times \left(\dfrac{1}{5}\right)}{1 - \left(\dfrac{1}{25}\right)}\right) + \tan^{- 1}\left(\dfrac{3}{4}\right)\right]

=cosec[tan⁡−1(512)+tan⁡−1(34)]= cosec \left[\tan^{- 1}\left(\dfrac{5}{12}\right) + \tan^{- 1}\left(\dfrac{3}{4}\right)\right]

=cosec[tan⁡−1(512+341−512×34)]= cosec \left[\tan^{- 1}\left(\dfrac{\dfrac{5}{12} + \dfrac{3}{4}}{1 - \dfrac{5}{12} \times \dfrac{3}{4}}\right)\right]

=cosec[tan⁡−1(5633)]=6556= cosec \left[\tan^{- 1}\left(\dfrac{56}{33}\right)\right] = \dfrac{65}{56}

option \left(1\right)$

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