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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2015 · Mathematics · Inverse Trigonometric Functions

Consider x=4 ^ -1 ((1)/(5)), y= ^ -1 ((1)/(70)) and z= ^ -1...

Consider x=4tan⁡−1(15),x=4 \tan ^{-1} \left(\frac{1}{5}\right),y=\tan ^{-1} \left(\frac{1}{70}\right)andandz=\tan ^{-1} \left(\frac{1}{99}\right)What is x−y+zx-y+z equal to?

Options

  1. Aπ2\frac{\pi}{2}
  2. Bπ3\frac{\pi}{3}
  3. Cπ6\frac{\pi}{6}
  4. Dπ4\frac{\pi}{4}

Correct answer

D. π4\frac{\pi}{4}

Step-by-step solution

x−y=tan⁡−182818450⇒tan⁡−1∣82818450∣+tan⁡−1(199)=tan⁡−1∣82818450+1991−82818450×199∣x-y=\tan ^{-1} \frac{8281}{8450} \Rightarrow \tan ^{-1}\left|\frac{8281}{8450}\right|+\tan ^{-1}\left(\frac{1}{99}\right)=\tan ^{-1}\left|\frac{\frac{8281}{8450}+\frac{1}{99}}{1-\frac{8281}{8450} \times \frac{1}{99}}\right|=tan⁡−1∣828269836550828269836550∣=1tan⁡−1=(1)=π4\begin{aligned} & =\tan ^{-1}\left|\frac{\frac{828269}{836550}}{\frac{828269}{836550}}\right|=1 \\ & \tan ^{-1}=(1)=\frac{\pi}{4} \end{aligned}∴\therefore \quad Option (D) is correct.
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