## anonymous one year ago Simplify sin^3(x)sec^2(x)-sin^2(x)

1. Nnesha

take out common factor

2. anonymous

there isn't one.

3. Nnesha

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

4. anonymous

sin^2

5. Nnesha

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

6. anonymous

$\sin^2x(sinxsec^2x-1)$

7. anonymous

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

8. Nnesha

gimme a sec :3 i'm working on it

9. anonymous

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

10. freckles

doesn't really seem like you can simplify it

11. Nnesha

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

12. 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)

13. freckles

14. Nnesha

ye

15. freckles

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

16. anonymous

no choices.

17. Nnesha

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

18. 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?

19. 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

20. 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?

21. freckles

it doesn't matter they are both ugly :p

22. Nnesha

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

23. anonymous

same. ok. thanks!

24. Nnesha

np :-)

25. freckles

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

26. freckles

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

27. 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"