Question

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



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Answer 1

Use the following identity:

cos(ao−90o)=sinaocos⁡(ao−90o)=sin⁡ao

Here is how. You know that

A + B = 180 - C

(A + B)/2 = 90 -C/2

c/2 = 90 - (A + B)/2

cos ( C/2) = cos ( 90 - (A + B)/2) = cos ( (A + B)/2 - 90) = sin ( (A + B)/2 )

where the last step used the identity given above, and the penultimate step used the fact that the cosine is an even function [ cos (a) = cos (-a) ].