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If α + β = 90°, then the value of (1 – sin²α) (1 – cos²α) × (1 + cot²β) (1 + tan²β) is
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- 1
- - 1
- 0
- 2
Correct Option: A
(1 – sin² α) (1 – cos²α) (1 + cot²β) (1 + tan² β)
= cos² α . sin² α . cosec² beta; sec²β
= (cos² α . cosec² β) (sin² α . sec² β)
= (cos² α . sec² α) (sin² &alpha . cosec² α) = 1
[α + β = 90° ⇒ β = 90° – α cosec β = cosec (90° – α)
= sec α ; sec β = sec (90° – α )
= cosec α, sin α . cosec α
= cos α . sec α = 1]
