cos C-cos D=2sin(C+D)/(2)sin(D-C)/(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 , show that : cosA-cosB+cosC-cosD=4sin( (A+B)/(2)) sin( (A+D)/(2)) cos( (A+C)/(2)) .

If A+B+C+D=2pi , show that : cosA-cosB+cosC-cosD=4sin( (A+B)/(2)) sin( (A+D)/(2)) cos( (A+C)/(2)) .

In quadrilateral ABCD, if sin((A+B)/(2))cos((A-B)/(2))+sin((C+D)/(2))cos((C-D)/(2))=2 then find the value of sin(A)/(2)sin(B)/(2)sin(C)/(2)sin(D)/(2)

In quadrilateral ABCD if sin((A+B)/(2))cos((A-B)/(2))+sin((C+D)/(2))cos((C-D)/(2))=2 , then find the value of "sin"(A)/(2)"sin"(B)/(2)"sin"(C)/(2)"sin"(D)/(2) .

Prove that : sinC-sinD = 2 cos frac (C+D)(2) sin frac (C-D) (2) .

If ( cos (A+B))/( cos (A-B)) =( sin (C+D))/( sin (C -D)) then prove that tan A tan B tan C + tan D=0 ................. A) 0 B) -1 C) sqrt3 D) 1

ln a quadrilateral ABCD if sin((A+B)/2)cos((A-B)/2)+sin((C+D)/2)cos((C-D)/2)=2, then sin(A/2)sin(B/2)sin(C/2)sin(D/2) has the value equal to (a)1/8 (b)1/4 (c)1/(2sqrt2) (d)1/2