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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 AskiitiansExpert-IITD Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
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
AskiitiansExpert-IITD
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