Cot cot everywhere

Geometry Level 3

( cot ⁡ B + cot ⁡ C ) ( cot ⁡ C + cot ⁡ A ) ( cot ⁡ A + cot ⁡ B ) ( \cot B+ \cot C)(\cot C + \cot A) (\cot A + \cot B)

If A , B A,B and C C are angles of a triangle with non-zero area, which of these expressions in the answer choices is equivalent to the trigonometric expression above?

1 1 sec ⁡ A 2 sec ⁡ B 2 sec ⁡ C 2 \sec \frac A2 \sec \frac B2 \sec \frac C2 csc ⁡ A csc ⁡ B csc ⁡ C \csc A \csc B \csc C sec ⁡ A sec ⁡ B sec ⁡ C \sec A \sec B \sec C tan ⁡ A tan ⁡ B tan ⁡ C \tan A \tan B \tan C

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Ashwin Kumar by Ashwin Kumar , 21, India

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1 solution

Ashwin Kumar
Oct 4, 2015

(cot B + cot C) (cot C + cot A) (cot A + cot B) =

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