Which of the following are identities? check all that apply.A tanx-tany=(sin(x-y))/(cosxcosy)B 1-tanxtany= (sin(x+y))/(sinxsiny)C tan (x-(pi/4))=tanx-1)D cos (x+(pi/6))=-sin(x-(pi/3))
Accepted Solution
A:
Answer:A and D.Step-by-step explanation:(sin(x-y))/(cosxcosy)(sinxcosy - cosxsiny) / cosxcosy= sinx / cosx - siny/cosy= tanx - tany. So A is an identity.B. (sin(x+y))/(sinxsiny) = sinx cosy + cosx siny / sinxsiny= cosy/siny + cosx/sinx= 1/tany + 1/tanx which is not identical with 1-tanxtany.C. tan ( x - pi/4) = ( tan x - 1) / (1 + tanx) : - not identical to tanx - 1.D. cos( x + (pi/6) = cosxcos(pi/6) - sinxsin(pi/6) = 0.866cosx - 0.5sinx - sin(x - (pi/3) = -(sinxcos(pi/3) - cosxsin(p/3)) = - (0.5sinx - 0.866cosx0 = 0.866cos x - 0.5sinx.which are identical.