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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

If (A+B)=1 and 2 (A-B)=1 , where 0 < A, B < (π)/(2) , then what is...

If sin⁡(A+B)=1\sin (A+B)=1 and 2sin⁡(A−B)=12 \sin (A-B)=1, where 0<A,B<π20 < A, B < \frac{\pi}{2}, then what is tan⁡A:tan⁡B\tan A: \tan B equal to?

Options

  1. A1:21: 2
  2. B2:12: 1
  3. C1:31: 3
  4. D3:13: 1

Correct answer

D. 3:13: 1

Step-by-step solution

sin⁡(A+B)=1⇒A+B=π2....(i)sin⁡(A−B)=12⇒A−B=π6....(ii)\begin{aligned} & \sin (A+B)=1 \\ & \Rightarrow A+B=\frac{\pi}{2} \quad ....\mathrm{(i)}\\ & \sin (A-B)=\frac{1}{2} \Rightarrow A-B=\frac{\pi}{6} \quad ....\mathrm{(ii)} \end{aligned} Solving equation (i) and (ii) we get A=π3 and B=π6∴tan⁡Atan⁡B=tan⁡π3tan⁡(π6)=313=3:1\begin{aligned} & A=\frac{\pi}{3} \text{ and } B=\frac{\pi}{6} \\ & \therefore \frac{\tan A}{\tan B}=\frac{\tan \frac{\pi}{3}}{\tan \left(\frac{\pi}{6}\right)}=\frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=3: 1 \end{aligned}
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