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))

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.