Question

if cotB/2=a+c/b find the angle A​

Answer 1

Answer:

A=π/2 .(It took me 14 minutes to type.Pls mark as brainliest)

Step-by-step explanation:

Using the sine law we can rewrite the assumption as

sinA+sinCsinB=cotB2  

We can now use the sum-to-product formula and remove the denominator that can be rewritten as  2sin(B/2)cos(B/2) , yielding

2sinA+C2cosA−C2=2cos2B2  

Since  A+C=π−B , we get

cosB2cosA−C2=cos2B2  

and therefore, being  cos(B/2)≠0 ,

cosA−C2=cosB2  

If  A≥C  this entails  A−C=B , so  A=B+C  and therefore  A=π/2 .