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Jobisdone [24]
3 years ago
15

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
Mathematics
1 answer:
tresset_1 [31]3 years ago
7 0
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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