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prove the following cot2A.cot2B+cot2B.cot2C+cot2C.cot2A=1

prove the following cot2A.cot2B+cot2B.cot2C+cot2C.cot2A=1

Grade:10

1 Answers

Arun
25763 Points
3 years ago
Dear Aryan
 
a + b + c = π; so (a + b) = π - c 
==> cot(a + b) = cot(π - c) = -cot(c) 

==> {cot(a)*cot(b) - 1}/{cot(a) + cot(b)} = -cot(c) 
Simplifying the above, 
cot(a)*cot(b) + cot(b)*cot(c) + cot(c)*cot(a) = 1 
 
 
Regards
Arun(askIITians forum expert)

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