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