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Geometry Level 2

Evaluate

( 2 − sec ⁡ 2 1 ∘ ) ( 2 − sec ⁡ 2 2 ∘ ) . . . ( 2 − sec ⁡ 2 8 9 ∘ ) (2-\sec^2 1 ^\circ)(2-\sec^2 2^\circ)...(2-\sec^2 89^\circ)


The answer is 0.

Alan Yan by Alan Yan , 20, USA

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1 solution

Alan Yan
Aug 10, 2015

sec ⁡ 45 ◦ = 2 ⟹ 2 − sec ⁡ 2 45 ◦ = 0 \sec 45◦ = \sqrt{2} \implies 2-\sec^2 45 ◦ = 0 Therefore the whole expression gets cancelled, resulting in the answer being 0 \boxed{0} .

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