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Prove that (1+tan1^(@))(1+tan2^(@))....(...

Prove that `(1+tan1^(@))(1+tan2^(@))....(1+tan4 5^(@))=2^(23)`

A

`2^(21)`

B

`2^(22)`

C

`2^(23)`

D

`2^(25)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+tantheta)(1+tan(45-theta)) = (1+tantheta) (1+(1-tantheta)/(1+tantheta)) = 2`
`(1+tan1^(@))(1+tan44^(@)) = 2 etc`
so product `= 2^(22) (1+tan45^(@)) = 2^(23)`
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