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Simplify sqrt(a^2-(a*sinx)^2)

 

\( \sqrt{a^2-(asin\theta)^2}\)

 Apr 12, 2016
 #1
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Simplify sqrt(a^2-(a*sinx)^2)

 

\(\begin{array}{rcll} \sqrt{ a^2 - [a \cdot \sin(x) ]^2 } &=& \sqrt{ a^2 - a^2 \cdot \sin^2(x) } \\ \sqrt{ a^2 - [a \cdot \sin(x) ]^2 }&=& \sqrt{ a^2 \cdot [ 1 - \sin^2(x) ] } \\ && \sin^2(x) + \cos^2(x) = 1 \qquad \text{ or }\qquad \cos^2(x) = 1 - \sin^2(x)\\ \sqrt{ a^2 - [a \cdot \sin(x) ]^2 }&=& \sqrt{ a^2 \cdot \cos^2(x) } \\ \mathbf{\sqrt{ a^2 - [a \cdot \sin(x) ]^2 } } & \mathbf{=} & \mathbf{a \cdot \cos(x) } \end{array}\)

 

laugh

 Apr 12, 2016

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