Find the value of \(\displaystyle{\cot{{\left({16}\right)}}}{\cot{{\left({44}\right)}}}+{\cot{{\left({44}\right)}}}{\cot{{\left({76}\right)}}}-{\cot{{\left({76}\right)}}}{\cot{{\left({16}\right)}}}\)

Boston Fitzgerald

Boston Fitzgerald

Answered question

2022-04-07

Find the value of cot(16)cot(44)+cot(44)cot(76)cot(76)cot(16)

Answer & Explanation

convinto44re

convinto44re

Beginner2022-04-08Added 9 answers

The idea is to exploit the identity
cot(α+β)=cotαcotβ1cotα+cotβ
With α=16,  β=44, we get for instance
cot16cot44=(cot16+cot44)cot60+1
Similarly,
cot44cot76=(cot44+cot76)cot120+1
and
cot(16)cot76=(cot(16)+cot76)cot60+1
Note cot(θ)=cotθ. All that is left to compute the sum of these three expressions, observing that cot60=cot120.

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