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If (1 + sin A) (1 + sin B) (1 + sin C) = (1 – sin A) (1 – sin B) (1 – sin C), 0 < A, B, C < (π / 2) then each side is equal to
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- sin A sin B sin C
- cos A cos B cos C
- tan A tan B tan C
- 1
Correct Option: B
(1 + sin A) (1 + sin B) (1 + sin C) = (1 – sin A) . (1 – sin B) (1 – sin C) = x (Let)
∴ x . x = (1 + sin A) (1 + sin B) (1 + sin C) (1 – sin A) (1 – sin B) (1 – sin C)
⇒ x² = (1 – sin² A) (1 – sin² B) (1 – sin² C)
⇒ x² = cos²A . cos²B . cos²C
⇒x = ± cos A . cos B . cos C
| ∵ 0 < A, B, C < | 2 |
∴ x = cos A . cos B . cos C
