Q176 / 270 · NDA 2012 (Phase 1) · Mathematics

Let $\sin (A+B)=1$ and $\sin (A-B)=1 / 2$, where $A, B$ $\in\left[0, \frac{\pi}{2}\right]$. What is $\tan (A+2 B) \cdot \tan (2 A+B)$ equal to?

  • A
    -1
  • B
    0
  • Correct answer
    C
    1
  • D
    2

Solution

$\begin{aligned} & \tan \left(120^{\circ}\right) \cdot \tan \left(150^{\circ}\right) \\ & \tan \left(90^{\circ}+30^{\circ}\right) \tan \left(90^{\circ}+60^{\circ}\right) \\ & \cot 30^{\circ} \cdot \cot 60^{\circ} \\ & \sqrt{3} \cdot \frac{1}{\sqrt{3}}=1\end{aligned}$

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

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