Question

in triangle abc express sigma r1 cot(a/2) in terms of s.​

Answer 1

We know that ,

(i) r1 = s × tan A/2,

(ii) r2 = s × tan B/2

(iii) r3 = s × tan C/2

Given: r1 cot A/2 + r2 cot B/2 + r3 cot C/2

= s × tan A/2 cot A/2 + s × tan B/2 cot B/2 + s × tan C/2 cot C/2

= s + s + s

= 3s