SOLUTION: Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigometric function. cos(tan-1 x)

Question 324168: Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigometric function.
cos(tan-1 x)
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you draw a triangle, you'll find that the two legs are 'x' and '1' which will make the hypotenuse to be . The opposite leg is 'x' and the adjacent leg is '1' which means that or simply that . Take the arctangent of both sides to get (note: this is a simplified view of the arctangent function)

So essentially, . So because the adjacent side is 1 unit long and the hypotenuse is , this means that

So

Again, a drawing really helps you see why this is true.
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