Question

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that   x.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7Bx%5E2-36%7D%20%7D%7Bx%7D%20" id="TexFormula1" title=" \frac{ \sqrt{x^2-36} }{x} " alt=" \frac{ \sqrt{x^2-36} }{x} " align="absmiddle" class="latex-formula">     0 ≤ θ < π/2.   
x=6secФ

Answer 1

After substituting:
$\frac{\sqrt{36sec^2 \theta - 36}}{6 sec \theta}$
Factor out the 36, allowing the 6's to cancel
$\frac{ \sqrt{sec^2 \theta - 1}}{sec \theta}$
Use trig identity:
sec^2 - 1 = tan^2
$\frac{\sqrt{tan^2 \theta}}{sec \theta} = \frac{tan \theta}{sec \theta} = sin \theta$