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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2022 · Mathematics · Trigonometric Ratios & Identities

If α+ β=1- α · β , where then which of the following is one of the...

If tan⁡α+tan⁡β=1−tan⁡α⋅tan⁡β\tan \alpha+\tan \beta=1-\tan \alpha \cdot \tan \beta, where then which of the following is one of the values of (α+β)(\alpha+\beta) ?

Options

  1. Aπ6\frac{\pi}{6}
  2. Bπ4\frac{\pi}{4}
  3. Cπ3\frac{\pi}{3}
  4. Dπ2\frac{\pi}{2}

Correct answer

B. π4\frac{\pi}{4}

Step-by-step solution

tan⁡α+tan⁡β=1−tan⁡α⋅tan⁡βtan⁡α+tan⁡β1−tan⁡α⋅tan⁡β=1⇒tan⁡(α+β)=tan⁡π4⇒α+β=π4\begin{aligned} & \tan \alpha+\tan \beta=1-\tan \alpha \cdot \tan \beta \\ & \frac{\tan \alpha+\tan \beta}{1-\tan \alpha \cdot \tan \beta}=1 \\ \Rightarrow & \tan (\alpha+\beta)=\tan \frac{\pi}{4} \\ \Rightarrow & \alpha+\beta=\frac{\pi}{4}\end{aligned}
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