If x and y are the two sides of a square and $x = (1 + sin A) (1 + sin B) (1 + sin C) = (1 - sin A) (1 - sin B) (1 - sin C),$
show that each side is equal to $\pm cos A cos B cos C .$

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Solution

If $x = y$ , then $x^{2} = x y$ .
$∴ x^{2} = (1 - {sin}^{2} A) (1 - {sin}^{2} B) (1 - {sin}^{2} C)$
$= {cos}^{2} A {cos}^{2} B {cos}^{2} C$
$∴ x = \pm cos A cos B cos C = y$ .

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