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Model Paper 2 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 21 Mark
MCQ
If $A - B =\frac{\pi}{4}$, then $(1+\tan A )(1-\tan B )$ is equal to
  • A
    2
  • B
    $0$
  • C
    1
  • D
    3
✓

Answer

(a) 2
Explanation: $\tan (A-B)=\tan \frac{\pi}{4}$
$\Rightarrow \frac{\tan A-\tan B}{1+\tan A \tan B}=1$
$\Rightarrow \tan A=\tan B=1+\tan A \tan B \ldots$ (i)
Now, 
$\begin{array}{l}(1+\tan A)(1-\tan B)=1+\tan A=\tan B=\tan A \tan B \\ =1+1+\tan A \tan B=\tan A \tan B \text { (Using eq. (i)) } \\ =2\end{array}$

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