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AKASH PAL Grade:
```        (1+TAN1)(1+TAN2).....................(1+TAN45)
=?```
7 years ago

## Answers : (1)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
```										Dear Akash,
Solution:-  Club the terms like this-
[(1+tan1)(1+tan44)] * [(1+tan2)(1+tan43)] * [(1+tan3)(1+tan42)].......[(1+tan22)(1+tan23)]*[(1+tan45)]
= [(1+(tan1+tan44) + (tan1)(tan44)]  * [(1+(tan2+tan43) + (tan2)(tan43)]......[(1+(tan22+tan23) + (tan22)(tan23)]* 2
Since, tanA + tan B = tan(A+B) [1- (tanA)(tanB)]. So, (tan1 +tan44) = tan(45) [1- (tan1)(tan44)] = [1- (tan1)(tan44)]. Doing it for all terms and putting them in above expression will give-
[(1+(1- (tan1)(tan44))  + (tan1)(tan44)]  * [(1+(1- (tan2)(tan43))  + (tan2)(tan43)]......[(1+(1- (tan22)(tan23))  + (tan22)(tan23)]* 2
= (2)*(2)*(2)......(2)*(2) = 223 [ANS].                          Please  feel free to post as many doubts on our discussion forum as you can. If  you find any questionDifficult to understand - post it here  and we will get you the answer and detailed solution very quickly. We are all  IITians and here to help you in your IIT JEE preparation.All the best Akash!!!Regards,Askiitians  ExpertsPriyansh Bajaj
```
7 years ago
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