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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2018 · Mathematics · Trigonometric Ratios & Identities

If α+ β=0= α+ β , where 0 < β < α < 2 π , then which one of the...

If sin⁡α+sin⁡β=0=cos⁡α+cos⁡β\sin \alpha+\sin \beta=0=\cos \alpha+\cos \beta, where 0<β<α<2π0 < \beta < \alpha < 2 \pi, then which one of the following is correct?

Options

  1. Aα=π−β\alpha=\pi-\beta
  2. Bα=π+β\alpha=\pi+\beta
  3. Cα=2π−β\alpha=2 \pi-\beta
  4. D2α=π+2β2 \alpha=\pi+2 \beta

Correct answer

B. α=π+β\alpha=\pi+\beta

Step-by-step solution

sin⁡α+sin⁡β=0=cos⁡α+cos⁡βsin⁡α+sin⁡β=0⇒sin⁡α=−sin⁡β⇒sin⁡α=sin⁡(π+β)⇒α=π+β\begin{aligned} & \sin \alpha+\sin \beta=0=\cos \alpha+\cos \beta \\ & \sin \alpha+\sin \beta=0 \\ & \Rightarrow \sin \alpha=-\sin \beta \\ & \Rightarrow \sin \alpha=\sin (\pi+\beta) \\ & \Rightarrow \alpha=\pi+\beta\end{aligned}
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