CAn someone explain how you get from:

sinx cosx^2 - sinx to sinx (cos^2x-1) to -sinx (1-cos^2x) to -sinx( sin^2x) to -sin^3x

and help me with factoring this equation:

sec^3x-sec^2x-secx+1

Thank you in advance(Bow)

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- Apr 28th 2008, 05:29 PM>_<SHY_GUY>_<Fundamental identities
CAn someone explain how you get from:

sinx cosx^2 - sinx to sinx (cos^2x-1) to -sinx (1-cos^2x) to -sinx( sin^2x) to -sin^3x

and help me with factoring this equation:

sec^3x-sec^2x-secx+1

Thank you in advance(Bow) - Apr 28th 2008, 05:44 PMo_O

sin x was factored out of the expression just as you would if you had something like

(-1 was factored out of the bracketed expression)

Recall that:

Substituting it in, we get:

since

----------------------------

Focusing on the red, let's factor out and for the blue, let's factor out -1:

Factor out (sec x - 1):

And hopefully the expression in purple reminds you of a certain identity. - Apr 28th 2008, 05:48 PM>_<SHY_GUY>_<
so from that i use the pythagorean identities multiply, and thats it right?

- Apr 28th 2008, 05:49 PMo_O
I'm not sure what you mean by what you wrote. What I was referring to was this identity:

- Apr 28th 2008, 05:55 PM>_<SHY_GUY>_<
which is derived from the pythagorean identity: sin^2+cos^2 = 1

and from there you multiply