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If (1+ tan 1) (1+tan 2)…..(1+tan45) = 2^n , then the value of n is…?? (a). 21 (b). 22 (c). 23 (d). 24

If (1+ tan 1) (1+tan 2)…..(1+tan45) = 2^n , then the value of n is…?? (a). 21 (b). 22 (c). 23 (d). 24

Chetan Mandayam Nayakar
312 Points
9 years ago

Perhaps, the formula tan((π/4)+θ)=(1+tan(theta))/(1-tan(theta)) may help.

Hope it works

Swapnil Saxena
102 Points
9 years ago

(1+ tan1) = 1+tan(45-44) = 1+ (tan(45) - tan(44))/1+tan(45)tan(44)  = 1+ ((1-tan44)/(1+tan44)) ==> 2/(1+tan(44))

Thus the above qproblem can be rewritten as

(2/(1+tan(44)))(2/(1+tan(43)))...(2/(1+tan(23))) * (1+tan(23))(1+tan(24))(1+tan(25))...(1+tan(45))

Can be simplified as (2*2*2...22 times)*(2) = 2^23

Thus the value of n is 23

vinay chaudhary
18 Points
9 years ago

since,(1+tan1)can be written as (1+tan(45-44)

on solving ,

we get (1+(1-tan44)/(1+tan44))

then , multiply the second last term

(1+(1-tan44)/(1+tan44))*(1+tan44)=2

similarly, all other terms can be solved.

Vaishal Shah
50 Points
9 years ago
if A+B=45 then (1+tanA)(1+tanB)=2.. So,the ans. Is 23.