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Simplify the following expression: cot(b-c)cot(c-a)+cot(c-a)cot(a-b)+cot(a-b)cot(b-c)

Simplify the following expression:
cot(b-c)cot(c-a)+cot(c-a)cot(a-b)+cot(a-b)cot(b-c)
 

Grade:11

1 Answers

Arnab
26 Points
3 years ago
let x= b-c,  y= c-a,  z= a-b
then x+y+z= b-c+c-a+a-b
 or,   x+y+z=0
 or,   x+y=-z
 or,   cot(x+y)= cot(-z)
 or,   (cot x • cot y – 1)/(cot y+ cotx)= -cot z
 or,   (cot x • cot y – 1)= –cot z (cot y+ cot x)
 or,   cot x•cot y -1= -cot y• cot z – cot z• cot x
 or,   cot x• cot y+ cot y• cot z+ cot z• cotx=1
or,     cot(b-c)cot(c-a)+cot(c-a)cot(a-    b)+cot(a-b)cot(b-c)=1

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