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Question : 21 of 160
Marks:
+1,
-0
Solution:
(1+tan‌1∘)(1+tan‌2∘)(1+tan‌3∘)...
(1+tan‌45∘)
Considering the following two terms
(1+tan‌x)(1+tan(45∘−x))
‌=1+tan‌x+tan(45∘−x)+tan‌x⋅tan(45∘−x)
‌=1+[tan‌x+tan(45∘−x)]+tan‌x⋅tan(45∘−x)
‌=1+tan(x+(45∘−x))⋅[1−tan‌x⋅tan(45∘−x)]
‌‌‌+tan‌x⋅tan(45∘−x)
‌=1+[1−tan‌x⋅tan(45∘−x)]+tan‌x⋅tan(45∘−x)
‌=1+1=2
‌=(2)22⋅(1+tan‌45∘)
‌=222⋅21=223=2n
‌∴‌‌n=23
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