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.
