If alpha beta 90 deg then the value of 1 ndash sin2 alpha 1 ndash cos2 alpha times 1 cot2 beta 1 tan...........

Quantitative Aptitude ( CCS) Trignometry

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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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Explanation:

As per the question, α + β = 90°,
∴ α = 90° – β.
(1 – sin²α) (1 – cos²α) × (1 + cot²β)(1 + tan²β)
[ ? 1 + tan²β = sec²β and 1 + cot²β = coesce²β ]
⇒ (1 – cos²β)(1 – sin²β) × cosec²β × sec²β
[? sin²α=sin²(90 – β) = cos²β and cos²α = cos²(90 – β) = sin²β ]
∴ sin²β . cos²β × 1/cos²β x 1/sin²β = 1
[ ? (1 – cos²β) = sin²β and (1 – sin²β) = cos²β ]