Question

If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = ______.

पर्याय

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Answer 1

If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = 1.

Explanation:

We know that if A + B + C = π, then tan A + tan B + tan C = tan A tan B tan C

`\implies 1/(tanB tanC) + 1/(tanA tanC) + 1/(tanA tan B)` = 1

`\implies` cot B cot C + cot A cot C + cot A cot B = 1