simplify cot(b-c)cot(c-a)+cot(a)cot(a-b)+cot(a-b)cot(b-c)
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substitute the values of alpha beta gamma to get the exact eq
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Step-by-step explanation:
let, x= A-B
y= B-C
z= C-A
\therefore x+y+z= A-B+B-C+C-A
\therefore x+y+z= 0
\therefore x+y= -z
\therefore cot(x+y)= cot(-z)
\therefore (cot x • cot y - 1)/(cot y + cot x)= -cot z
\therefore cot x• cot y -1 = -cot z(cot y + cot x)
\therefore cot x• cot y -1 = -cot z• cot y - cot z• cot x
\therefore cot x• cot y + cot z• cot y + cot z• cot x= 1
\therefore cot(A-B).cot(B-C)+cot(C-A).cot(B-C)+cot(C-A)+cot(A-B)=1
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