Question

PLZ PLZ HELP!!!!!! The expression cos(A+pi) - sin(A + pi) can be simplified to

a) sin(A) - cos(A)
b) sin(A) + cos(A)
c) cos(A)- sin(A)
d) -sin(A) - cos(A)

Answer 1

Sin(A+B) = SinACosB + CosASinB
Cos(A+B) = CosACosB - SinASinB

Note pi is taken as pi radians = 180 degrees. Cospi = Cos180 = -1.
Sinpi = Sin 180 = 0

Cos(A+pi) = CosACospi - SinASinpi = (CosA) * (-1) - (SinA) *(0) = -CosA.
Sin(A+pi) = SinACospi + CosASinpi = (SinA)* (-1) + (CosA) * (0) = -SinA.

Cos(A+pi) - Sin(A+pi) = -CosA - -SinA = -CosA + SinA = SinA - CosA.

Answer = (a).