How do you simplify this trigonometric equation??

Question

Hi there! I'm sure that this is pretty simple, but regardless, I'm not really sure where to begin. I'll give 2 examples of the kinds of problems that I don't know how to solve. If you could please tell me HOW to do it and WHY you're doing each step, rather than just the answer, that would be great because I have the answer key already... I just don't know how you arrive at the answer. :) Thanks!

(sin x)^4 - (sin x)^2
--------------------------
sec x


and

(cos w)(sin w ^2) + (cos w)^3
----------------------------------------
sec w


Thanks again! I'll pick a best answer TODAY!

Both of those answers actually sucked so bad that I'm contemplating deleting my question just so that neither of you get an extra 10 points.

Answer 1

(sin² x)(sin² x - 1)
----------------------- =
sec x

sin² x (-cos²x)
-------------------- =
(1/cos x)

-sin² x cos³ x

(cos w)(sin² w) + cos³ w
--------------------------------- =
sec w

cos w [sin² w + cos² w]
-------------------------------- =
(1/cos w)

cos² w [ 1 ] =
cos² w

Answer 2

1st one. Just factor out (sin x)^2

(sin x)^2[ (sin x)^2 - 1] cos x =
-(sin x)^2 (cos x)^3

2nd one

(cos w (sin w)^2 + (cos w)^3) cos w =
(cos w)^2 ( (sin w)^2 + (cos w)^2) =
(cos w)^2

Answer 3

well you know sin x must be greater than 4, and so it must also be greater than 4...problem is you still don't know WHAT it is. Is there a way to tell? Sorry, I am terrible at math.

Answer 4

Just figure out which one is a derived value and convert to base units. I'll give you a hint, it starts with s..........

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