Question 1012334
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Use a right triangle to write the following expression as an algebraic expression. 
Assume that x is positive and in the given inverse trigonometric function tan(arccos 2x)
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<pre>
Let {{{alpha}}} = arccos(2x).

It means that {{{cos(alpha)}}} = 2x and {{{alpha}}} lies in the 1st or in the 2nd quadrant.

We need to express {{{tan(alpha)}}} via x.


Since {{{cos(alpha)}}} = 2x, {{{sin(alpha)}}} = {{{sqrt(1 -(2x)^2)}}} = {{{sqrt(1-4x^2)}}}.

Therefore, {{{tan(alpha)}}} = {{{(sin(alpha))/(cos(alpha))}}} = {{{(sqrt(1-4x^2))/(2x)}}}.

<U>Answer</U>. {{{tan(alpha)}}} = {{{(sqrt(1-4x^2))/(2x)}}}.
</pre>

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Your formulation is not perfect.
The right formulation is 


"Find {{{tan(alpha)}}} if {{{arccos(alpha)}}} = 2x."