- anonymous

Simplify sin^3(x)sec^2(x)-sin^2(x)

- jamiebookeater

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- Nnesha

take out common factor

- anonymous

there isn't one.

- Nnesha

yes there is
let's say sin = x
and sec = y
so x^3 y - x^2 what is common factor ?

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## More answers

- anonymous

sin^2

- Nnesha

yep right sin^2( ) what should be in the parentheses ?? :-)

- anonymous

\[\sin^2x(sinxsec^2x-1)\]

- anonymous

I need to simplify it more. How would I do that?

- Nnesha

gimme a sec :3 i'm working on it

- anonymous

ok. :) I've tried a lot of different ways myself and it never gets real simple.

- freckles

doesn't really seem like you can simplify it

- Nnesha

i guess try this identity 1+tan^2 =sec^2
otherwise that's it sin^2(sin(x)sec^2-1)

- freckles

for some reason I read sin^2(x)sec^2(x)-sin^2(x)
at first
sin^2(x)(sec^2(x)-1)
sec^2(x)tan^2(x)

- freckles

but we had sin^3(x)sec^2(x)-sin^2(x)

- Nnesha

ye

- freckles

maybe we are just suppose to rewrite it (not really simplify)
are there are choices @AEB047 ?

- anonymous

no choices.

- Nnesha

or you can write sin^3 as sin^2 times sin

- freckles

earlier you said you needed to simplify more
how did you know that
like is this something you are trying to simplify to exactly?

- Nnesha

\[ \sin^3(x)\sec^2(x)-\sin^2(x)\]
write sec^2 = 1/cos^2
\[\sin(x) \times \sin^2(x) \times \frac{ 1 }{ \cos^2(x) } - \sin^2(x)\]
sin^2/cos^2 = tan^2

- anonymous

ok, so we can end up with:
\[\frac{ \sin^3x }{ \cos^2x }-\sin^2x\]
or
\[\sin^2x(\frac{ sinx }{ \cos^2x }-1)\]
or
\[\tan^2xsinx-\sin^2x\]
Which one is the most simplified, do you think?

- freckles

it doesn't matter
they are both ugly :p

- Nnesha

i'll go with de last one :P
i hate fraction >.<

- anonymous

same. ok. thanks!

- Nnesha

np :-)

- freckles

@AEB047 can I ask where you got this question from:
Simplify sin^3(x)sec^2(x)-sin^2(x)

- freckles

Like did your teacher come up with it?
Was that the original problem?

- freckles

I'm just not convinced the "original problem" is actually the original problem
Because to me no simpler form has been given to the "original" unless your teacher has clearly defined the word "simplify"

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