How to calculate the value of tan-1 without using a calculator?
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Simply speaking, you can't.  You cannot work out the exact value.  However, you can approximate it by expanding it using the taylor expansion which gives that image

Although using this you would have to know what 25^5 is.  The further you expand the series, the closer the approximation is to the true value.

Chances are that you will not learn about these types of expansion unless you go to university to study maths. 

 

However, an additional way of working this out, is if this is looks something like this

arctan(x) = pi/4

in which case you can take tan of both sides to give 

x = tan(pi/4) 

by Level 3 User (4.6k points)

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