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UPSC NDA I 2012 Mathematics Paper

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For the next Three (3) questions that follow:

Let

\sin\; (A+B)=1

and

\sin\; (A-B)=\frac{1}{2}

, where

A, B

\in \left[0, \;\frac{\pi}{2}\right]

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Question : 26 of 120

Marks: +1, -0

What is

\tan (A+2B) \cdot \tan (2A+B)

$-1$
0
1
2

Solution:

\tan(120^{\circ}) \cdot \tan(150^{\circ})

\tan(90^{\circ}+30^{\circ}) \tan(90^{\circ}+60^{\circ})

\cot(30^{\circ}) \cdot \cot(60^{\circ})

\sqrt{3} \cdot \frac{1}{\sqrt{3}} = 1

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