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```        (1+tan 1)(1+tan 2)(1+tan 3)(1+tan 4)(1+tan 5)......................(1+tan 45)= 2^n
find the value of n
how?
prove by any theorem
```
6 years ago

419 Points
```
Dear Aritra
Here you have to make pairs such that sum of angle is 45 like  (1+tan1)(1+tan44) and (1+tan2)(1+tan43) etc there will be 22 pairs like  this and one single term 1+tan45 which is equal to two
you have to apply sin(90-A)=cosA etc
you can write 1+tanA=√2 sin(45+A)/cosA=√2 cos(45-A)/cosA
like for pair  (1+tan1)(1+tan44)=(√2 sin(45+1)/cos1)*(√2 cos(45-44)/cos44)
sin46 and cos44 will cancel the value of this pair will be 2. like this 22 pairs are there.it will be 222 and last term is 1+tan45=2
so it will be 223
hence n=23

All the best.
AKASH GOYAL

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```
6 years ago
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