First slide

Trigonometric Identities

Question

If $(1 - \sin A) (1 - \sin B) (1 - \sin C) = (1 + \sin A)$ $(1 + \sin B) (1 + \sin C)$ , then each sides is equal to

Easy

A

$\pm \cos A \cos B \cos C$
B

0
C

$\pm \sin A \sin B \sin C$
D

1

Solution

Multiply both the sides by
$(1 - \sin A) (1 - \sin B) (1 - \sin C)$ to obtain
$\begin{array}{l} (1 - \sin^{2} A)^{} (1 - \sin^{2} B)^{} (1 - \sin^{2} C)^{} \\ = \cos^{2} A \cos^{2} B \cos^{2} C \\ \Rightarrow (1 - \sin A) (1 - \sin B) (1 - \sin C) \\ = \pm \cos A \cos B \cos C \end{array}$

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