If $(1 + sin A) (1 + sin B) (1 + sin C) = (1 - sin A) (1 - sin B) (1 - sin C)$ ,then find the value of $(1 + sin A) (1 + sin B) (1 + sin C)$

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Solution

Let $P = (1 + sin A) (1 + sin B) (1 + sin C) = (1 - sin A) (1 - sin B) (1 - sin C)$
$\Rightarrow P^{2} = (1 + sin A) (1 + sin B) (1 + sin C) \times (1 - sin A) (1 - sin B) (1 - sin C)$
$\Rightarrow P^{2} = (1 - {sin}^{2} A) (1 - {sin}^{2} B) (1 - {sin}^{2} C) = {cos}^{2} A {cos}^{2} B {cos}^{2} C ∴ P = \pm cos A cos B cos C$

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