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aritra nandy Grade: 10
        (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
answer:-23
how?
prove by any theorem
6 years ago

Answers : (1)

AKASH GOYAL AskiitiansExpert-IITD
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


AskiitiansExpert-IITD


 


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6 years ago
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