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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2012 · Mathematics · Inverse Trigonometric Functions

If ^ -1 2, ^ -1 3 are two angles of a triangle, then what is the...

If tan⁡−12,tan⁡−13\tan ^{-1} 2, \tan ^{-1} 3 are two angles of a triangle, then what is the third angle?

Options

  1. Atan⁡−12\tan ^{-1} 2
  2. Btan⁡−14\tan ^{-1} 4
  3. Cπ/4\pi / 4
  4. Dπ/3\pi / 3

Correct answer

C. π/4\pi / 4

Step-by-step solution

θ1=tan⁡−12θ2=tan⁡−13,θ3=?θ1+θ2+θ3=180∘tan⁡−12+tan⁡−13+θ3=180∘tan⁡−1(2+31−2.3)+θ3=180∘tan⁡−1(5−5)+θ3=180∘135+θ3=180∘θ3=45.\begin{gathered}\theta_1=\tan ^{-1} 2 \\ \theta_2=\tan ^{-1} 3, \theta_3=? \\ \theta_1+\theta_2+\theta_3=180^{{}^{\circ}} \\ \tan ^{-1} 2+\tan ^{-1} 3+\theta_3=180^{{}^{\circ}} \\ \tan ^{-1}\left(\frac{2+3}{1-2.3}\right)+\theta_3=180^{{}^{\circ}} \\ \tan ^{-1}\left(\frac{5}{-5}\right)+\theta_3=180^{{}^{\circ}} \\ 135+\theta_3=180^{{}^{\circ}} \\ \theta_3=45.\end{gathered}
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