Why does this expression simplify to 1-sin(x)?

[Jbright1406]

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 doesn't explain what exactly happens. could someone please shed some light and explain what exactly happens

 

[Defennder]

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?

Edit: No, I misread!

 

[Jbright1406]

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

then the final answer being

1 over (1-sinx)

 

[Jbright1406]

[(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]

[(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.