Question

if a and b are acute angles such that sinA=4/5 and cosB=12/13, calculate, without using tables: sin(a-b)

Answer 1

`\sin \alpha = (4)/(5) \\ \cos \alpha = √(1-\sin^2 \alpha )= \sqrt{1- (16)/(25) } = \sqrt{ (9)/(25) }= (3)/(5) \\ \\ \cos \beta = (12)/(13) \\ \sin \beta = √(1-\cos^2 \beta )= \sqrt{1- (144)/(169) } = \sqrt{ (25)/(169) }= (5)/(13)`



`\\ \\ \sin (\alpha- \beta ) =\sin \alpha \cos \beta -\cos \alpha \sin \beta = (4)/(5)* (12)/(13)- (3)/(5)* (5)/(13) = (48)/(65)- (15)/(65)= (33)/(65)`

Answer:
sin(α-β) = 33/65