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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2010 · Mathematics · Inverse Trigonometric Functions

What is the value of ^ -1 (4)/(5)+2 ^ -1 (1)/(3) ?

What is the value of sin⁡−145+2tan⁡−113?\sin ^{-1} \frac{4}{5}+2 \tan ^{-1} \frac{1}{3} ?

Options

  1. Aπ3\frac{\pi}{3}
  2. Bπ2\frac{\pi}{2}
  3. Cπ4\frac{\pi}{4}
  4. Dπ6\frac{\pi}{6}

Correct answer

B. π2\frac{\pi}{2}

Step-by-step solution

2tan⁡−1(13)=tan⁡−1231−19=tan⁡−1342 \tan ^{-1}\left(\frac{1}{3}\right)=\tan ^{-1} \frac{\frac{2}{3}}{1-\frac{1}{9}}=\tan ^{-1} \frac{3}{4} Also sin⁡−145=tan⁡−143=cot⁡−134∴tan⁡−134+cot⁡−134=π2\sin ^{-1} \frac{4}{5}=\tan ^{-1} \frac{4}{3}=\cot ^{-1} \frac{3}{4}\therefore \tan ^{-1} \frac{3}{4}+\cot ^{-1} \frac{3}{4}=\frac{\pi}{2}
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