`cos(A-B).cos (A+B) +sin(A-B).sin(A+B)=?`

Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)

Prove that: (cos(A-B)+sinA-cos(A+B))/(sin(A+B)+cosA-sin(A-B))=tanA

Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B+C)+sin(-A+B+C)+sin(A-B+C)-"sin"(A+B-C))=cot C

cos (A +B) + sin (A -B) = 2 sin (45 ^(@) + A) cos ( 45 ^(@) + B).

let a=cosA+cosB-cos(A+B) and b=4sin(A/2)sin(B/2)cos((A+B)/2) Then a-b is

Prove that: sin(B-C)cos(A-D) + sin(C-A) cos (B-D) + sin(A-B) cos(C-D) = 0

Solve sinA.cos(A-B)-cosA.sin(A-B)

Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) ((A -B)/( 2 )).

Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC b) cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC

If A + B + C = pi then prove that cos A + cos B + cos C = 1 + 4 sin(A/2) .sin(B/2).sin(C/2)