ELE 28If 3 tan A tan B = 1, prove that2 cos (A + B) = cos (A-B).

1.	ELE 28If 3 tan A tan B = 1, prove that2 cos (A + B) = cos (A-B).
Answer» 3 (sinA/cosA) (sinB/cosB) = 1 (sinA sinB/cosA cosB) = 1/3 (2sinAsinB/2cosA cosB) = 1/3 [cos(A-B) -cos (A+B) ] / [ cos(A+B) +cos (A-B) ] = 1/3 now cross multiplication 3cos(A-B) -3cos (A+B) = cos(A+B) +cos (A-B) 3cos(A-B) -cos (A-B) = cos(A+B) + 3cos (A+B) 2 cos(A-B) = 4 cos (A+B) cos(A-B) = 2 cos (A+B)

Answer»

3 (sinA/cosA) (sinB/cosB) = 1

(sinA sinB/cosA cosB) = 1/3

(2sinAsinB/2cosA cosB) = 1/3

[cos(A-B) -cos (A+B) ] / [ cos(A+B) +cos (A-B) ] = 1/3

now cross multiplication

3cos(A-B) -3cos (A+B) = cos(A+B) +cos (A-B)

3cos(A-B) -cos (A-B) = cos(A+B) + 3cos (A+B)

2 cos(A-B) = 4 cos (A+B)

cos(A-B) = 2 cos (A+B)

Discussion