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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2013 · Mathematics · Inverse Trigonometric Functions

What is ^ -1 ((1)/(2))+ ^ -1 ((1)/(3))equal to?

What is tan⁡−1(12)+tan⁡−1(13)equalto?\tan ^{-1} \left(\frac{1}{2}\right)+\tan ^{-1} \left(\frac{1}{3}\right)equal to?

Options

  1. Aπ2\frac{\pi}{2}
  2. Bπ3\frac{\pi}{3}
  3. Cπ4\frac{\pi}{4}
  4. Dπ6\frac{\pi}{6}

Correct answer

C. π4\frac{\pi}{4}

Step-by-step solution

We know that tan⁡−1m+tan⁡−1n=tan⁡−1(m+n1−m⋅n)Here,\tan ^{-1} m+\tan ^{-1} n=\tan ^{-1} \left(\frac{m+n}{1-m \cdot n}\right) Here,m=12,\frac{1}{2},n=13\frac{1}{3}tan⁡−1(12)+tan⁡−1(13)=tan⁡−1(12+131−12⋅13)=tan⁡−1(55)\begin{aligned}& \tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1} \left(\frac{1}{3}\right)\\ & =\tan ^{-1}\left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}\right)=\tan ^{-1}\left(\frac{5}{5}\right) \end{aligned}$=\tan ^{-1}(1)=\frac{\pi}{4}
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