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Trigonometry> We have to find x in this problem . I hav...

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We have to find x in this problem . I have tried this to solve my question please tell me what next or another method

Surjeet Singh Kushwah , 7 Years ago

Grade 12

1 Answers

Arun

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 (askIITians forum expert)

Last Activity: 7 Years ago

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