1. The problem statement, all variables and given/known data The two vectors a and b lie in the xy plane and make angles α and β with the x axis. a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity cos(α-β)=cos(α)cos(β)+sin(α)sin(β) b)By similarly evaluating a X b prove that sin(α-β) = sin(α)cos(β) - cos(α)sin(β) c)Now let vector a make an angle -α with the x axis and find a similar expression for cos(α+β) 2. Relevant equations a • b = abcos(θ) a • b = a1b1+a2b2 3. The attempt at a solution I drew the vectors a and b with their appropriate angles to the x-axis... The angle between the vectors is (α-β) so I have a •b = abcos(α-β) but I have no idea how to relate this to the trig identities!