Simplify the following expression:cot(b-c)cot(c-a)+cot(c-a)cot(a-b)+cot(a-b)cot(b-c)
Durwa Thakur , 6 Years ago
Grade 11
Trigonometry> Simplify the following expression: cot(b-...
1 AnswersArnab
Last Activity: 6 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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