What is this TRIG identity called. see attachment.

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What is this TRIG identity called. see attachment.

Mathematics
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I'm not sure if there is a specific name for this identity
how would I explain it though
I guess you could say "composition of a trig function and another inverse" ? I'm not sure
oh you want to know how they got that identity?
yeah
here let me give you an example
tan(arccos(x)) let theta = arccos(x) so cos(theta) = x = x/1 agreed?
\[\tan(\cos^-1(1/2)\]
yes agreed
so we can create this right triangle |dw:1438215201249:dw|
|dw:1438215224912:dw|
cos(theta) = x/1 cosine deals with adjacent over hypotenuse
so we can add these labels |dw:1438215259342:dw|
what is the missing side equal to (in terms of x) ?
1^2-x^2
it will be the square root of that
|dw:1438215360088:dw|
@jim_thompson5910 how do we gate the base of absolute value of x
tan(arccos(x)) turns into tan(theta) this is because I let theta = arccos(x) calculating tan(theta) gives \[\Large \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{1-x^2}}{x}\]
for some reason, and I don't know why, they made the denominator be |x| instead of just x. My guess is that they wanted to force tan(arccos(x)) to be positive. However, tan(arccos(x)) is only positive when x is positive
So it should be \[\Large \tan(\arccos(x)) = \frac{\sqrt{1-x^2}}{x}\]

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