math trigo

alfa+bita = thita & tan x ratio tan y= x ratio y then prove that sin alfa- bita = x- y ratio x+y sinthita

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  1. that's alpha, beta, theta

    If I read you right, we have

    θ = α+β
    tanx/tany = x/y
    prove: sin(α-β) = (x-y)/(x+y) sinθ

    well, sinθ = sin(α+β)
    so now we can say we want

    sin(α-β)/sin(α+β) = (x-y)/(x+y)

    note that

    sin(x-y)+sin(x+y) = 2sinx*cosy
    sin(x-y)-sin(x+y) = -2cosx*siny

    Things should work out from here

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