A) 1
B) \[-\,\,1\]
C) 2
D) \[-\,\,2\]
Correct Answer: C
Solution :
\[(1+\tan A)(1+\tan B)=(1+\tan A)[1+\tan \,\,(45{}^\circ -A)]\] \[=(1+\tan A)\left[ 1+\frac{\tan 45{}^\circ -\tan A}{1+\tan 45{}^\circ \tan A} \right]\] |
\[=(1+\tan A)\left[ 1+\frac{1-\tan A}{1+\tan A} \right]\] |
\[=(1+\tan A)\left[ 1+\frac{\tan A+1-\tan A}{1+\tan A} \right]\] |
\[=(1+\tan A)\left[ \frac{2}{1+\tan A} \right]=2\] |
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