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If (1 + sinα) (1 + sinβ) (1 + sinγ) = (1 – sinα) (1 – sinβ) (1 – sinγ), then each side is equal to (SSC CGL 2nd Sit. 2013)
- a)± cos α cos β cos γ
- b)± sin α sin β sin γ
- c)± sin α cos β cos γ
- d)± sin α sin β cos γ
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If (1 + sinα) (1 + sinβ) (1 + sinγ) = (1 – sin&...
(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 – sin γ)
x2 = (1 – sin2 α) (1 – sin2 β) (1 – sin2 γ)
x2 = cos2 α. cos2β.cos2 γ
⇒ x = ± cos α. cos β . cos γ
∴ x.x = (1 + sin α) (1– sin α) (1 + sin β)
(1 – sin β) (1 + sin γ) (1 – sin γ)
x2 = (1 – sin2 α) (1 – sin2 β) (1 – sin2 γ)
x2 = cos2 α. cos2β.cos2 γ
⇒ x = ± cos α. cos β . cos γ
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If (1 + sinα) (1 + sinβ) (1 + sinγ) = (1 – sinα) (1 – sinβ) (1 – sinγ), then each side is equal to (SSC CGL 2nd Sit. 2013)a)± cos α cos β cos γb)± sin α sin β sin γc)± sin α cos β cos γd)± sin α sin β cos γCorrect answer is option 'A'. Can you explain this answer?
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