Trigonometry that will make you go nuts.

Geometry Level 2

Evaluate (cot x)(cot 2x) - (cot 2x)(cot 3x) - (cot 3x)(cot x)


The answer is 1.

Ashtik Mahapatra by Ashtik Mahapatra , 22, India

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2 solutions

Adarsh Kumar
May 11, 2014

cosx•cos2x/sinx•sin2x -cos2x•cos3x/sin2x•sin3x - cos3x•cosx/sin3x•sinx=(cosx•cos2x•sin3x - cos2x•cos3x•sinx - cos3x•cosx•sin2x)/sinx•sin2x•sin3x=(cosx•sinx - cos2x•cos3x•sinx)/sinx•sin2x•sin3x=( cosx-cos2x•cos3x)/sin2x•sin3x=[cos(3x-2x)-cos2x•cos3x]/sin2x•sin3x=1.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Bhargav Varshney
May 11, 2014

Tan 2x = 2tan x/{1-(tan^2 x)} and Tan 3x = {3tan x - (tan^3 x)}/{1-3(tan^2 x)}.

Using these two formulae , we can solve and conclude the answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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