Question

show that equations sin(x+y) =sinx+siny is not an identity

Answer 1

sin(x+y)=sinxcosy+sinycosx
its the sin of a double angle.
if we replace y=x we get sin(x+x)=sin(2x)
then if we replace y=x in sinxcosy+sinycosx
we get sinxcosx+cosxsinx=2(sinxcosx)
therefore sin(2x)=2sinxcosx

Answer 2

you could also show this with a counter-example, x = 30degrees, y = 60 degrees..............................sin(x+y) = sin(90) = 1.....................sin(x)+sin(y) = sin(30)+sin(60) = 0.5+0.866 = 1.366

Answer 3

and also sin(x) the x is the argument so sin(x+y)=doesnot=sinx+siny and is not distributed