Prove that `(cosA-cosB)^2+(sin A-sin B)^2=4sin^2((A-B)/2)`

Prove that (cos x- cos y ) ^2 + ( sin x - sin y ) ^2 = 4 sin ^2"" ((x-y))/(2)

Prove that cosA -cosB -cosC =1-4sin(A/2)cos(B/2)cos(C/2) ,if A+B+C= pi

If triangleABC is a right triangle and if angleA=pi/2 , then prove that (i) cos^(2) B+cos^(2)C=1 (ii) sin^(2) B+sin^(2) C=1 cos B-cos C=-1+2 sqrt2 cos""B/2sin ""C/2

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

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

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

In any triangle prove that a^2 =(b+c)^2 sin^2 (A/2) +(b-c)^2 cos^2 (A/2)

Show that (1+sinA)/(cosA)+(cosB)/(1-sinB)=(2sinA-2sinB)/(sin(A-B)+cosA-cosB)

Prove that (sin (A-B))/(sin (A+B))=(a^(2)-b^(2))/(c^(2))

Prove that sin""A/2+sin ""B/2+sin ""C/2=1+4 sin ((pi-A)/(4))sin"" (pi-B)/(4)sin ((pi-C)/(4))," If A+B+C "=pi