SOLUTION: Simplify the given function by referring to the appropriate triangle or trigonometric identity. {{{cos[tan^(-1)(x)]}}}

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Question 210770This question is from textbook Single Variable Calculus
: Simplify the given function by referring to the appropriate triangle or trigonometric identity.
cos%5Btan%5E%28-1%29%28x%29%5D This question is from textbook Single Variable Calculus

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the given function by referring to the appropriate triangle or trigonometric identity.
cos%5Btan%5E%28-1%29%28x%29%5D
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Draw a right triangle.
Let "a" be one of the small angles.
Let a = tan^-1(x)
Then the tan(a) = x/1
Lebel the side opposite "a" as "x", and the adjacent side as one.
Then, using Pythagoras", the hypotenuse is sqrt(1+x^2)
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Then cos(a) = 1/sqrt(1+x^2)
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Cheers,
Stan H.