Question

If A,B,C are in Arithmetic Progression,then the correct relation is? Answer with detailed steps. Question in Attachment

Answer 1

Answer:

1) cot B= (sin A - sin C) / (cos C - cos A)

Step-by-step explanation:

Given that A,B and C are in A.P

=> 2B = A+C [ relation between A,B and C }

consider ,

cot B = cot (2B/2)

= cot (A+C)/2

= cos (A+C)/2 / sin (A+C)/2

= cos (A+C)/2 / sin (A+C)/2 X { 2sin[(A-C)/2] / 2[sin(A-C)/2] }

= 2. cos(A+C)/2 . sin[(A-C)/2]

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2. sin(A+C)/2 . sin[(A-C)/2]

= (sin A - sin C) / - (cos A - cos C)

cot B = (sin A - sin C) / (cos C - cos A)