Question

Verify the identity:
csc x - csc x cos^2x=sinx

Answer 1

factor out a cscx. what do you have now?

Answer 2

One thing that always helps is to put in terms of \(\sin\) and \(\cos\).
\[
\csc x-\csc x \cos^2x = \frac1{\sin x}-\frac{\cos^2x}{\sin x}
\]

Answer 3

So how did you get the\[\frac{ \cos ^{2}x }{ \sin x }\]

Answer 4

Oh, nvm.
What would you do after that step?

Answer 5

Well, it's a fraction, so you can combine them. Fortunately the denominator is already the same, so it works out easily.

Answer 6

\[
\frac1{\sin x}-\frac{\cos^2x}{\sin x} = \frac{1-\cos^2x}{\sin x}
\]

Answer 7

At this point, you need to remember the Pythagorean identity. \[
\sin^2x+\cos^2x=1
\]

Answer 8

Do you think you would be able to do the rest?

Answer 9

Not really. I don't get how the pythagorean identity applies to the next step.

Answer 10

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

Answer 11

That is how it will apply.

Answer 12

Oh, okay. I get it. Thank you.