in triangle abc, if

Question

sin c= (sin a + sin b )/ ( cos a + cos b )

prove that triangle abc is a right-angle triangle.

Answer 1

In a right triangle, assuming a and b are the acute angles, then a + b = 90 degrees and sin b = cos a, and sin a = cos b. Therefore
sin c = (sin a + sin b/(cos a + cos b)
= (cos a + cos b)/(cos a + cos b) = 1
Therefore c is a right angle. This proves that the relation is true for right triangles, if c is the right angle, but does not prove it is not true for other triangles.