Question

if ABCD is a cyclic quadrilateral and A, B, C, D are it's interior angles, then prove that :sinA/2+sinB/2=cosC/2+cosD/2

Answer 1

Angle A+c=180.......equation 1
b + d =180...equation 2
in equation 1
a=180-c
sina =sin(180-c)
sina/2=sin(90-c/2
sina/2=cosc/2.......equation 3
similarly
sinb/2=cosd/2......equation 4
adding equation 3and 4
sina/2+sinb/2=cosc/2+cosd/2

Answer 2

answer is HENCE, PROVED