# Thread: (1+tan 1)(1+tan 2).....(1+tan 45)=

1. ## (1+tan 1)(1+tan 2).....(1+tan 45)=

(1+tan 1)(1+tan 2).....(1+tan 45)=

What should i be knowing to find the answer to this ?

2. ## Re: (1+tan 1)(1+tan 2).....(1+tan 45)=

Originally Posted by Raj917
(1+tan 1)(1+tan 2).....(1+tan 45)=

What should i be knowing to find the answer to this ?
First, you can write it as $(1+\tan 0^\circ)(1+\tan 1^\circ)(1+\tan 2^\circ)\cdots(1+\tan 45^\circ)$ (because the additional term at the beginning is equal to 1).

Next, pair off the terms from the beginning and the end:

$\bigl((1+\tan 0^\circ)(1+\tan 45^\circ)\bigr) \bigl((1+\tan 1^\circ)(1+\tan 44^\circ)\bigr)\cdots\bigl((1+\tan 22^\circ)(1+\tan 23^\circ)\bigr).$

Then see if you can work out the value of each of those paired products.

3. ## Re: (1+tan 1)(1+tan 2).....(1+tan 45)=

Originally Posted by Opalg
First, you can write it as $(1+\tan 0^\circ)(1+\tan 1^\circ)(1+\tan 2^\circ)\cdots(1+\tan 45^\circ)$ (because the additional term at the beginning is equal to 1).

Next, pair off the terms from the beginning and the end:

$\bigl((1+\tan 0^\circ)(1+\tan 45^\circ)\bigr) \bigl((1+\tan 1^\circ)(1+\tan 44^\circ)\bigr)\cdots\bigl((1+\tan 22^\circ)(1+\tan 23^\circ)\bigr).$

Then see if you can work out the value of each of those paired products.

Thank you sir the answer is 2^23

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# (1 tan 1) (1 tan 2) (1 tan 3) ... (1 tan 44) (1 tan 45) =

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