The Student Room Group
Reply 1
mc_watson87
2 tan^-1 (x-1) = tan^-1 x

What's this? Do you need to prove it or solve it?
Reply 2
Gaz031
What's this? Do you need to prove it or solve it?

Lol, soz, find value of x
Reply 3
I assume he wants to solve it, as it's not an identitiy.

2 arctan(x-1) = arctan(x)
x = tan[2 arctan(x-1)]
= (2tan[arctan(x-1)])/(1 - tan²[arctan(x-1)])
= [2(x-1)]/[1-(x-1)²]
etc.
Reply 4
2 tan^-1 (x-1) = tan^-1 x
tan [2 tan^-1 (x-1)] = tan[tan^-1 x]
tan [2 tan^-1 (x-1)] = x
now use the identity for tan2x:
x = 2tan[tan^-1 (x-1)] / { 1- tan²[tan^-1 (x-1)] }
x = 2[x-1] / [1 - ( x - 1 )² ]
now solve the equation and find x

x = 1.54

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