Question

If A + B + C = 180 then
cot B cot C + cot C cot A + cot A cot B =​

Answer 1

Answer:

The answer is 1

Step-by-step explanation:

A+B+C=180°

A=180°-(B+C)

tanA=-tan(B+C)

cotB cotC + cotC cotA + cotA cotB

=

$1 \div \tan(b) \tan(c) + 1 \div \tan(c) \tan(a) + 1 \div \tan(a) \tan(b) = {\tan(a) + \tan(b) + \tan(c) } \div \tan(a )\tan(b) \tan(c) = {- \tan(b + c) + \tan(b) + \tan(c) } \div - \tan(b + c) \tan(b) \tan(c) = 1$