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If (l + sin α) (l + sinβ) (l + sin γ) = (1 – sin α)(l – sinβ) (l – sin γ), then each side is equal to
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- ± cos α cos β cos γ
- ± sin α sin β sin γ
- ± sin α cos β cos γ
- ± sin α sin β cos γ
Correct Option: A
(1 + sin α) (1 + sin β) (1 + sin
γ) = (1 – sin α) (1–sin β) (1– sin γ) = x
∴ x.x = (1 + sin α) (1 – sin α) (1 + sin β) (1 – sin β)(1 + sin γ)(1– sinγ)
= (1 – sin²α) (1 – sin²β)(1 – sin²γ)
= cos²α . cos²β . cos²γ
∴ x = ± cos α . cos β . cos γ
