Prove that : `(cos A - cos B)^2 + (sin A - sin B)^2 = 4sin^2\ (A-B)/2`

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

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

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

Prove that (1 + sin A) / (cos A) + (cos B) / (1-sin B) = (2sin A-2sin B) / (sin (AB) + cos A-cos B)

Prove that: ((cos A+cos B)/(sin A-sin B))^(n)+((sin A+sin B)/(cos A-cos B))^(n)={2cot^(n)((A-B)/(2)),quad if niseven0,if nisodd

prove that ((cos A+cos B)/(sin A-sin B))^(n)+((sin A+sin B)/(cos A-cos B))^(n)=2cot^(n)((A-B)/(2)),n is even

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

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

For any triangle ABC,prove that a cos A+b cos B+c cos C=2a sin B sin C

cos2B + cos2A-cos2C = 1-4sin A sin B cos C