Question

If cos A = `13/14` and cos B = `1/7` where A, B are acute angles prove that A – B = `pi/3` 

Answer 1

cos A = `13/14`, cos B = `1/7`

sin A = `sqrt(1 - cos^2"A")`

`= sqrt(1 - 1/49) = sqrt(48/49) = sqrt48/7 = (4sqrt3)/7`

cos(A – B) = cos A cos B + sin A sin B

`= 13/14 xx 1/7 + (3sqrt3)/14 xx (4sqrt3)/7`

`= 13/98 + 36/98 = 49/98 = 1/2`

cos(A – B) = cos 60°

A – B = 60° = `pi/3`