SOLUTION: Make the trigonometric substitution x = a tan θ for −π/2 < θ < π/2 and a > 0. Simplify the resulting expression. (x^2/{{{sqrt (a2 + x2)}}}) I do not know how to start

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Question 1159331: Make the trigonometric substitution
x = a tan θ for −π/2 < θ < π/2 and a > 0.
Simplify the resulting expression.
(x^2/)
I do not know how to start this problem! What am I substituting?? HELP.

Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

In the denominator, which is  ,  you should replace x by  .


It is "how to start".


Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

We are given

Wherever you see an 'x', replace it with . Then simplify.



Make the replacements





Factor out the a^2

Break up the root

Works because a > 0



The equation 1+tan^2 = sec^2 is one variation of the pythagorean trig identity

Secant is positive when theta is between -pi/2 and pi/2









One pair of cosine terms divide and cancel









------------------------------------------------------------

Since and , we can say

only when a > 0 and -pi/2 < theta < pi/2.

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