# Explain why this simplifies

ok, i have this and know what it should simplify to, but why?

(1-sin(x))(sin(x))-(cos(x))(0-cos(x))

i know it simplifies to

1-sin(x)

but my book doesnt explain what exactly happens. could someone please shed some light and explain what exactly happens

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Defennder
Homework Helper
I think you mistyped something. It doesn't simplify to that. Try for example x =pi/4.

atyy
I think you mistyped something. It doesn't simplify to that. Try for example x =pi/4.
I'm parsing his message as:

(1-sinx)(sin2x+cos2x)

Does that make sense?

thats what i kept seeing.

i see it simplifies to one.

the answer in the book shows the answer i previously gave over (1-sinx)^2

1 over (1-sinx)

[(1-sinx)(-sinx)-cosx(0-cosx)]/(1-sinx)^2

then
(1-sinx)/(1-sinx)^2

then the final being
(1)/(1-sinx)

PS sorry for the double posting

Defennder
Homework Helper
[(1-sinx)(-sinx)-cosx(0-cosx)]/(1-sinx)^2
That minus sign, which was absent in your original post, makes the whole world of difference. To simplify, just expand the numerator out and apply a trigo identity.