IMPOSSIBLE MATH QUESTION

\[(1+\tan(1^\circ))(1+\tan(2^\circ))(1+\tan(3^\circ))(1+\tan(4^\circ)) \cdots (1+\tan(45^\circ))=?\]

Find the value.

well u can also do this without a calculator take t an 1 = t an ( 45 − 44 ) = 1 + t an 44 1 − t an 44 ​
then ( 1 + t an 1 ) = ( 1 + 1 + t an 44 1 − t an 44 ​ ) = 1 + t an 44 2 ​ therefore similarly ( 1 + t an 1 ) ( 1 + t an 2 ) ... ( 1 + t an 22 ) = 1 + t an 44 2 ​ 1 + t an 43 2 ​ 1 + t an 42 2 ​ .. 1 + t an 23 2 ​ = ( 1 + t an 44 ) ( 1 + t an 43 ) ( 1 + t an 42 ) ... ( 1 + t an 23 ) 2 22 ​ then ( 1 + t an 1 ) ... ( 1 + t an 45 ) = ( 1 + t an 44 ) ( 1 + t an 43 ) ( 1 + t an 42 ) ... ( 1 + t an 23 ) 2 22 ​ ( 1 + t an 23 ) ( 1 + t an 24 ) ... ( 1 + t an 45 ) = 2 22 ( 1 + t an 45 ) = 2 23 = 8388608

Answered by madankapoor10 | 2024-06-10

(1+tan 1)(1+ tan 2)...(1+tan 45)=(1+0.017455)(1+0.03492)...(1+1)=8388608.11

Answered by Anity | 2024-06-10

The product P = ( 1 + tan ( 1 ∘ )) ( 1 + tan ( 2 ∘ )) ⋯ ( 1 + tan ( 4 5 ∘ )) evaluates to 2 23 = 8388608. This is derived through pairing the terms based on the symmetry of the tangent function. Each paired product contributes a value of 2, and with 22 pairs plus the term at 45 degrees, the final value is established.
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Answered by madankapoor10 | 2024-12-24