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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2019 · Mathematics · Trigonometric Ratios & Identities

If 2 A-3 B-1 , then what is (A-B) equal to?

If 2tan⁡A−3tan⁡B−12 \tan \mathrm{ A}-3 \tan \mathrm{ B}-1, then what is tan⁡(A−B)\tan (\mathrm{A}-\mathrm{B}) equal to?

Options

  1. A15\frac{1}{5}
  2. B16\frac{1}{6}
  3. C17\frac{1}{7}
  4. D19\frac{1}{9}

Correct answer

C. 17\frac{1}{7}

Step-by-step solution

 Given : 2tan⁡A=1⇒tan⁡A=12 and tan⁡B=13∵tan⁡(A−B)=tan⁡A−tan⁡B1+tan⁡⋅Atan⁡B⇒tan⁡(A−B)=12−131+12⋅13=1676=17\begin{aligned} & \text{ Given : } 2 \tan A=1 \\ & \Rightarrow \tan A=\frac{1}{2} \text{ and } \tan B=\frac{1}{3} \\ & \because \tan (A-B)=\frac{\tan A-\tan B}{1+\tan \cdot A \tan B} \\ & \Rightarrow \tan (A-B)=\frac{\frac{1}{2}-\frac{1}{3}}{1+\frac{1}{2} \cdot \frac{1}{3}}=\frac{\frac{1}{6}}{\frac{7}{6}}=\frac{1}{7}\end{aligned}
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