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 $(1 - \sin A)(1 - \sin B)(1 - \sin C)$, 

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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