How do you verify ${cos}^{2} x + {cos}^{2} (\frac{π}{2} - x) = 1$ $cos^2x + cos^2(pi/2 - x) = 1$ ?

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How do you verify ${cos}^{2} x + {cos}^{2} (\frac{π}{2} - x) = 1$ $cos^2x + cos^2(pi/2 - x) = 1$ ?

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Answer 1 · 2016-05-02T21:30:32

Using the identities

$cos (x - \frac{π}{2}) = sin (x)$ $cos(x-pi/2) = sin(x)$
$cos (- x) = cos (x)$ $cos(-x) = cos(x)$
${cos}^{2} (x) + {sin}^{2} (x) = 1$ $cos^2(x)+sin^2(x) = 1$

we have:

${cos}^{2} (x) + {cos}^{2} (\frac{π}{2} - x) = {cos}^{2} (x) + {cos}^{2} (- (x - \frac{π}{2}))$ $cos^2(x)+cos^2(pi/2-x) = cos^2(x) + cos^2(-(x-pi/2))$

$= {cos}^{2} (x) + {cos}^{2} (x - \frac{π}{2})$ $=cos^2(x)+cos^2(x-pi/2)$

$= {cos}^{2} (x) + {sin}^{2} (x)$ $=cos^2(x)+sin^2(x)$

$= 1$ $=1$

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How do you verify ${cos}^{2} x + {cos}^{2} (\frac{π}{2} - x) = 1$ $cos^2x + cos^2(pi/2 - x) = 1$ ?

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How do you verify cos^2x + cos^2(pi/2 - x) = 1cos2x+cos2(π2−x)=1cos^2x + cos^2(pi/2 - x) = 1?

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How do you verify ${cos}^{2} x + {cos}^{2} (\frac{π}{2} - x) = 1$ $cos^2x + cos^2(pi/2 - x) = 1$ ?