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.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.