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(1+tan1°)(1+tan2°)..................(1+tan45°)=2^n Find value of n?

(1+tan1°)(1+tan2°)..................(1+tan45°)=2^n
Find value of n?

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1 Answers

Arun
25757 Points
4 years ago
Dear Imran
 
tan45 = tan (1 + 44) = tan1 + tan44 / 1 – tan1 tan44
 
1 – tan 1 tan44 = tan1 + tan44
 
(1 + tan1) (1 + tan44) = 2
 
similarly
(1 + tan2) (1 + tan43) = 2
 
 
 
Now
 
2 * 2* 2 * …...22 times * (1 + tan45)
 
 = 223
 
Regards
Arun

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