Question

ABCD is a quadrilateral then...show that cosec(A+C/4) = sec(B+D/4)

Answer 1

Step-by-step explaA,B,C and D are the angles of quadrilateral. To show that cos(A+B)/2 = cos(C+D)/2.  Since A,B,C and D are the anglea of a quadrilateral,

A+B+C+D = 360.  Therefore  A+B = 360-(C+D)    Dividing by 2, we get:

(A+B)/2 = {360-(C+D)}/2 = 180 - (C+D)/2

cos(A+B)/2 = Cos{180-(C+D)/2}  

Cos(A+B)/2 = -cos(C+D)/2, as cos (180-theta) = -cos(theta)

Add cos(C+D)/2 to both sides:

Cos(A+B)/2 +Cos(C+D)/2