How do I solve
tan^-1 (x) = 2tan^-1 (x-1)?
The answer should be 1.54.
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How do I solve
tan^-1 (x) = 2tan^-1 (x-1)?
The answer should be 1.54.
tan-1(x) = 2tan-1 (x-1)
Apply tan to both sides:
x = tan[2tan-1 (x-1)]
For simplicity, call y = tan-1 (x-1)
so that tan(y) = (x - 1) and x = tan(2y)
Now use the well known formula:
tan(2x) = 2 tan(x) / (1 - tan2x)
x = tan(2y) = 2tan(y) / (1 - tan2y) = 2(x - 1) / [1 - (x - 1)2]
... and the rest should be easy.
Well, maybe not that easy, as you come up with a third degree equation. I had to use numerical methods (e.g. the Newton-Raphson method) and got approx.Quote:
Originally Posted by krtxmrtz
x = 1.544
which corresponds to an angle of 88.45 deg.
Oo I forgot about the double angle forumla :rolleyes: Thanks. :D