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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2014 · Mathematics · Trigonometric Ratios & Identities

If A=2 and B=3 , then what is the value of A+B ?

If cot⁡A=2\cot \mathrm{A}=2 and cot⁡B=3\cot \mathrm{B}=3, then what is the value of A+BA+B ?

Options

  1. Aπ6\frac{\pi}{6}
  2. Bπ\pi
  3. Cπ2\frac{\pi}{2}
  4. Dπ4\frac{\pi}{4}

Correct answer

D. π4\frac{\pi}{4}

Step-by-step solution

cot⁡A=2∴tan⁡A=12and cot⁡B=3∴tan⁡B=13tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡A⋅tan⁡B=12+131−12×13⇒tan⁡(A+B)=56×65=1⇒tan⁡(A+B)=tan⁡π4⇒A+B=π4\begin{aligned} & \cot A=2 \therefore \tan A=\frac{1}{2} \\ & \text{and } \cot B=3 \therefore \tan B=\frac{1}{3} \\ & \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \cdot \tan B}=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \times \frac{1}{3}} \\ & \Rightarrow \tan (A+B)=\frac{5}{6} \times \frac{6}{5}=1 \\ & \Rightarrow \tan (A+B)=\tan \frac{\pi}{4} \\ & \Rightarrow \quad A+B=\frac{\pi}{4}\end{aligned}
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