Question

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

Answer 1

take out common factor

Answer 2

there isn't one.

Answer 3

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

Answer 4

sin^2

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

gimme a sec :3 i'm working on it

Answer 9

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

Answer 10

doesn't really seem like you can simplify it

Answer 11

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

Answer 12

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)

Answer 13

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

Answer 14

ye

Answer 15

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

Answer 16

no choices.

Answer 17

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

Answer 18

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

Answer 19

\[ \sin^3(x)\sec^2(x)-\sin^2(x)\]
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

Answer 20

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?

Answer 21

it doesn't matter
they are both ugly :p

Answer 22

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

Answer 23

same. ok. thanks!

Answer 24

np :-)

Answer 25

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

Answer 26

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

Answer 27

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"