Let 0º < θ < 90º. (1 + cot2θ) (1+tan2θ) × (sinθ - cosecθ) (cosθ - secθ) is equal to:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. secθ cosecθ
(1 + cot2θ) (1+tan2θ) × (sinθ - cosecθ) (cosθ - secθ)
we know that, (1 + cot2θ) = cosec2θ and (1+tan2θ) = sec2θ.
cosec2θ × sec2θ × (sinθ - 1/sinθ)(cosθ - 1/cosθ)
(1/sin2θ) × (1/cos2θ) × [(sin2θ - 1)/sinθ] × [(cos2θ - 1)/cosθ]
= Cosecθ Secθ