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Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that   \(\frac{ \sqrt{x^2-36} }{x}\)     0 ≤ θ < π/2.   
x=6secФ

Verified Answer :

wizard123

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
\(\frac{\sqrt{tan^2 \theta}}{sec \theta} = \frac{tan \theta}{sec \theta} = sin \theta\)

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