cos C+cos D=2cos((C+D))/(2)cos((C-D))/(2)

Prove (i)cos C+cos D=2(cos(C+D))/(2)(cos(C-D))/(2) (ii)cosC-cosD =2sin(C+D)/2sin(D-C)/2

Assertion (A) : Suppose that alpha- beta is not an odd multiple of (pi)/(2) , m in R-{0,1) and (sin (alpha+beta))/(cos (alpha-beta))=(1-m)/(1+m) then Tan ((pi)/(4)-alpha)=m cot ((pi)/(4)- beta) Reason (R) : for all C,D, & R cos c+cos D= 2 cos ((C+D)/(2)) cos((C-D)/(2)) cos-cosD=-2sin ((C+d)/(2))sin ((C-D)/(2))

Prove (i)sin C+sin D=2(sin(C+D))/(2)(cos(C-D))/(2)(ii)sin C-sin D=2(sin(C-D))/(2)(cos(C+D))/(2)

If A + B + C + D = 2pi , prove that: cos A + cos B + cos C + cos D =-4"cos"(A+B)/(2)"cos"(A+C)/(2)"cos"(A+D)/(2)

Prove that : cos C +cosD = 2 cos frac (C+D)(2) cos frac (C-D) (2) .

In a quadrilateral if (sin (A + B)) / (2) (cos (AB)) / (2) + (sin (c + D)) / (2) + (sin (c + D)) / ( 2) (cos (cD)) / (2) = 2, then (cos A) / (2) (cos B) / (2) + (cos A) / (2) (cos c) / (2) + (cos A) / (2) (cos D) / (2) + (cos B) / (2) (cos C) / (2) + (cos B) / (2) (cos D) / (2) + (cos C) / (2) (cos D) / (2)

If A+B+C+D=360^(@) , the prove that cos 2A + cos 2B + cos 2C + cos 2D =4 cos (A+B) cos (A+C) cos (A+D)

If A,B,C,D are the angles of a quadrilateral then cos""((A+B)/(2))+ cos ""((C+D)/(2)) =

if ABCD0 is a quadrilatral then cos((A+B)/(2))+cos((C+D)/(2))=

(cos(A-B))/(cos(A+B))+cos(C+D)/(cos(C-D))=0 => tan A tan B tan C tan D =