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Question
If A − B = π/4, then (1 + tan A) (1 − tan B) is equal to
Options
2
1
0
3
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Solution
2
\[\tan(A - B) = \tan\frac{\pi}{4}\]
\[ \Rightarrow \frac{\tan A - \tan B}{1 + \tan A \tan B} = 1\]
\[ \Rightarrow \tan A - \tan B = 1 + \tan A\tan B . . . (1) \]
Now,
\[(1 + \tan A)(1 - \tan B ) = 1 + \tan A - \tan B - \tan A \tan B\]
\[ = 1 + 1 + \tan A\tan B - \tan A \tan B \left(\text{ Using eq }(1) \right)\]
\[ = 2\]
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