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How to solve this question please give me the way to this question

How to solve this question please give me the way to this question

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Grade:12

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
I have attached the solution here-
 
\\(tan^{-1}x)^2 + \left( \frac{\pi}{2} - tan^{-1}x\right)^2 = \frac{5\pi^2}{8} \\\\ Let\ tan^{-1}x = k \\\\ 2k^2 -\pi k + \frac{\pi^2}{4} - \frac{5\pi^2}{8} = 0 \\ 16k^2 -8\pi k - 3\pi^2 = 0 \\ 16k^2 -12\pi k+ 4\pi k - 3 \pi^2 = 0 \\ (4k-3\pi)(4k+\pi) = 0 \\ x = tan\left(\frac{3\pi}{4}\right), x = tan\left( \frac{-\pi}{4}\right) \\\\x = -1
 
In case of any query, please feel free to ask
 
Regards
Arun

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