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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2016 · Mathematics · Quadratic Equation

Given that α and β are the roots of the equation x^2+bx+c=0 with b...

Given that tan⁡α\tan \alpha and tan⁡β\tan \beta are the roots of the equation x2+bx+c=0\mathrm{x}^2+\mathrm{bx}+\mathrm{c}=0 with b≠0\mathrm{b} \neq 0. What is sin⁡(α+β)sec⁡αsec⁡β\sin (\alpha+\beta) \sec \alpha \sec \beta equal to?

Options

  1. Ab
  2. B–b
  3. Cc
  4. D–c

Correct answer

B. –b

Step-by-step solution

sin⁡(α+β)sec⁡αsec⁡β=sin⁡αcos⁡β+cos⁡αsin⁡βcos⁡αcos⁡β=tan⁡α+tan⁡β=−b\begin{aligned} & \sin (\alpha+\beta) \sec \alpha \sec \beta \\ & =\frac{\sin \alpha \cos \beta+\cos \alpha \sin \beta}{\cos \alpha \cos \beta} \\ & =\tan \alpha+\tan \beta \\ & =-b\end{aligned}
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