Prove that sin^2 A cos^2 B+cos^2 A sin^2 B+cos^2 A cos^2 B+sin^2 A sin^2 B=1

Prove that cos2A=cos^2 A -sin^2 A

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

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

Expand cos ( A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = (pi)/(2) .

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

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

If A+B+C=180^0 , prove that : cos^2, A/2 + cos^2, B/2 - cos^2, C/2 = 2cos, A/2 cos, B/2 sin, C/2

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

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

If A+B+C=pi prove that cos^(2) A+cos^(2) B+cos^(2) C=1 - 2cos A cos B cos C .