Question

combine the fractions and simplify to a multiple of a power of a basic trigonometric function
sinx/cot^2x-sinx/cos^2x?

Answer 1

can i change the sinx/cos^2x into tan^2x?

Answer 2

Hmm no. You can take ONE of the cosines, and change it to tanx*(1/cosx) But I dont know if that's the right way to go c: hmm

Answer 3

\[\large \frac{ \sin x }{ \cot^2 x }-\frac{ \sin x }{ \cos^2 x }=\frac{ \sin x }{ (\frac{ \cos^2 x }{ \sin^2 x }) }-\frac{ \sin x }{ \cos^2 x }\]
\[\large \frac{ \sin x }{ 1 }*\frac{ \sin^2 x }{ \cos^2 x }-\frac{ \sin x }{ \cos^2 x }\]

Answer 4

There are multiple ways to simplify it, since there are so many trig identities, so you might find a different way... but this is what I was thinking :3

Answer 5

\[\large \frac{ \sin^3 x - \sin x }{ \cos^2 x }\]

Answer 6

Confused about any of that so far? :D

Answer 7

how did you get sinx/1∗sin^2x/cos^2x

Answer 8

\[\large \frac{ \left(\frac{ a }{ b }\right) }{ \left(\frac{ c }{ d }\right) }=\frac{ a }{ b }*\frac{ d }{ c }\]

Answer 9

Remember how you can do that? when dividing fractions :D flip the bottom one and rewrite it as multiplication.

Answer 10

but the top wasn't a fraction yet it was sinx/ (cos^2x/sin^2x)

Answer 11

oh wait you put it over 1 to make it into a fraction huh?

Answer 12

\[\huge \frac{ \left(\sin x \right) }{ \left(\frac{ \cos^2 x }{ \sin^2 x } \right) }=\frac{ \left(\frac{ \sin x }{ 1 } \right) }{ \left(\frac{ \cos^2 x }{ \sin^2 x } \right) }\]

Answer 13

Yah hehe :3

Answer 14

I gotta go, so lemme post the rest of the steps, and you can at least look at them while I'm gone. I won't be here to answer questions though :c

Answer 15

okay

Answer 16

\[\large \frac{ \sin^3 x - \sin x }{ \cos^2 x }=\frac{ \sin x(\sin^2 x - 1) }{ 1-\sin^2 x }\]

Answer 17

Factored a sinx from each term in the top.
Rewrote cos^2 as 1-sin^2 using identity :D

Answer 18

Now if we factor a -1 ouch of each term in the top brackets, we'll have a nice easy cancellation.

Answer 19

\[\large \frac{ -\sin x(1-\sin^2 x) }{ 1-\sin^2 x }=-\sin x\]

Answer 20

Hopefully I didn't make a mistake in there :D heh

Answer 21

alright well thanks