MCQ
If $(1 + \sin A)(1 + \sin B)(1 + \sin C)$$ = (1 - \sin A)(1 - \sin B)(1 - \sin C),$ then each side is equal to
- A$ \pm \sin A\sin B\sin C$
- ✓$ \pm \cos A\cos B\cos C$
- C$ \pm \sin A\cos B\cos C$
- D$ \pm \cos A\sin B\sin C$
✓
Answer
Correct option: B.
$ \pm \cos A\cos B\cos C$
b
(b) Multiplying both sides by $(1 - \sin A)(1 - \sin B)(1 - \sin C)$,
(b) Multiplying both sides by $(1 - \sin A)(1 - \sin B)(1 - \sin C)$,
we have, $(1 - {\sin ^2}A)(1 - {\sin ^2}B)(1 - {\sin ^2}C)$
$ = {(1 - \sin A)^2}{(1 - \sin B)^2}{(1 - \sin C)^2}$
==> $(1 - \sin A)(1 - \sin B)(1 - \sin C) = \pm \cos A\cos B\cos C$
Similarly, $(1 + \sin A)(1 + \sin B)(1 + \sin C) = \pm \cos A\cos B\cos C$.
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