Question

Prove this CotA/2+cotB/2+cotC/2=CotA/2.CotB/2.CotC/2.

Answer 1

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