If \cos3A + \cos3B + \cos3C = 1 in a

Abbigail Robles

Abbigail Robles

Answered question

2022-04-22

If cos3A+cos3B+cos3C=1 in a triangle, find one of its length

Answer & Explanation

l3n4bananau6j

l3n4bananau6j

Beginner2022-04-23Added 12 answers

Hint
cos{3A}+cos{3B}+cos{3C}=1
4sin3C2sin3B2sin3A2=0
Hence the largest angle of triangle is 2π3 which can be either angle C or angle A. By applying cosine rule in each of these cases we get the value of AB as 399 or 945 respectively.
Note:
cos3A+cos3B+cos3C=1
2cos{3(AB)2}sin{3C2}2(sin{3C2})2=0
=sin3C2(cos3(AB)2+sin3C2)=0
sin3C2(cos3(AB)2cos3(A+B)2)=0
sin3C2sin3B2sin3A2=0

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