Prove this CotA/2+cotB/2+cotC/2=CotA/2.CotB/2.CotC/2.
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Answer:
Step-by-step explanation:
Using the ANGLE SUM PROPERTY-:
=> A + B + C = 180°
=> A/2 + B/2 + C/2 =90°
=> A/2 + B/2 = 90 - C/2
=> cot(A/2 + B/2) = cot(90 - C/2)
Using the formula
=>cot (A + B) = ((cot A)*(cot B) - 1) / ((cot A) + (cot B))
=> cot(A/2)cot(B/2) - 1/cot(B/2) + cot(A/2) = tanC/2
=> cot(A/2)cot(B/2) - 1/cot(B/2) +cot(A/2) = 1/cotC/2
=> cotA/2 cotB/2 cotC/2 - cotC/2 = cotB/2 + cotA/2
=> cotA/2 cotB/2 cotC/2 = cotA/2 + cotB/2 + cotC/2
=> cotA/2 + cotB/2 + cotC/2 = cotA/2 cotB/2 cotC/2
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