Q178 / 270 · NDA 2020 · Mathematics

If $\cot \alpha$ and $\cot \beta$ are the roots of the equation $x^2-3 x+2$ $=0$, then what is $\cot (\alpha+\beta)$ equal to ?

  • A
    $\frac{1}{2}$
  • Correct answer
    B
    $\frac{1}{3}$
  • C
    2
  • D
    3

Solution

Given equation: $x^2-3 x+2=0$ Sum of roots, $\cot \alpha+\cot \beta=-(-3)=3$ (i) Product of roots, $\cot \alpha \cdot \cot \beta=2$ (ii) Now, $\cot (\alpha+\beta)=\frac{\cot \alpha \cdot \cot \beta-1}{\cot \alpha+\cot \beta}=\frac{2-1}{3}=\frac{1}{3}$.

Hence, the correct answer is option: 'B'.

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