Question

simplify sinx-sinx cos^2x?

Answer 1

You would first want to extract the common factor, in this case, being sinx. Could you do that & show us what you get?

Answer 2

it would just be sin (-1+cos^2x) right?

Answer 3

it would until you replace \(1-\cos^2(x)\) by something else

Answer 4

No, when you remove sinx, you wouldn't get -1+cos^2x, since you are removing sinx, not -sinx.

Answer 5

@hayleybakess : Try it again & post your answer in this thread.

Answer 6

it would just be sin (1+cos
^2x) ?

Answer 7

And you would have to note that it is sinx, not sin, since sin is a function and cannot be computed on its own. So it would be:

sinx-sinx cos^2x = sinx(1-cos^2x)

Now, what do we know about 1-cos^2x? Does this seem familiar to you?

Answer 8

sin^2(x) + cos^2(x) = 1 ?

Answer 9

@hayleybakess : Yes, that's correct! So what can we get from this identity?

Answer 10

sin^2x=1-cos^2x so basically the left side of the equation now just equals sinx?

Answer 11

I was looking at the wrong thing!

Answer 12

No, you got the identity correct though - sin^2x = 1-cos^2x, so substitute this into the original equation we have above - what does that give you?

Answer 13

sinx-sinx cos^2x = sinx(1-cos^2x)
so now it would be:
sinx-sinx cos^2x= sinx(sin^2x)?

Answer 14

@shiraz14 ?

Answer 15

@hayleybakess : Yes, you're correct. Now what is sinx(sin^2x)?

Answer 16

I honestly don't know, is it Sin^3 x? @shiraz14

Answer 17

Yes, you're absolutely correct. :) Take a medal!

Answer 18

:) so then
sinx-sinx cos^2x= sin^3x
how do I simplify further?
@shiraz14

Answer 19

@hayleybakess : That's the final answer - there's nothing else to be done.