If $A, B$ are complementary angles, then ${cos}^{2} A + {cos}^{2} B$

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Solution

$c o s^{2} A + c o s^{2} B$
And $A$ and $B$ are complementary
So
$A + B = 90, A = 90 - B$
${(c o s (90 - B))}^{2} + c o s^{2} B$
$= {sin}^{2} B + {cos}^{2} B = 1$

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