## anonymous one year ago Trig / Pre Cal/identities Am I on the right path? Please do not give the answer. Here is the problem $$\frac{(\sin x- \cos x)*2}{cos} = \sec x - \cos x$$ I am working on the left side and need to prove it equals the right. This is what I have done so far $$\frac{(\sin^2 x - 2(\cos x)(\sin x)+\cos^2 x}{\cos x} = \sec x - \cos x$$ Am I going about this the right way because I don't see where to go from here. Thank you.

1. anonymous

It is suppose to be Trig / Pre Cal/identities Am I on the right path? Please do not give the answer. Here is the problem $$\frac{(\sin x- \cos x)^2}{cos} = \sec x - \cos x$$ I am working on the left side and need to prove it equals the right. This is what I have done so far $$\frac{(\sin^2 x - 2(\cos x)(\sin x)+\cos^2 x}{\cos x} = \sec x - \cos x$$ Am I going about this the right way because I don't see where to go from here. Thank you.

2. anonymous

This is where I am at. Am I on the right path and where do I go from here because I do not see anything. $$\frac{\sin^2 x - 2(\cos x)(\sin x)+\cos^2 x}{\cos x} = \sec x - \cos x$$

3. anonymous

Sorry

4. anonymous

5. Nnesha

hmm well....... i guess both sides are not equal

6. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Nixy Made a mistake $$\color{blue}{\text{End of Quote}}$$ what ?? :-)

7. anonymous

It is suppose to be $$\frac{(\sin x- \cos x)^2}{cos} = \sec x - 2\sin x$$ And I am at $$\frac{\sin^2 x - 2(\cos x)(\sin x)+\cos^2 x}{\cos x} = \sec x - 2\sin x$$

8. anonymous

I was typing it in too fast and made a boo boo. Sorry about that.

9. anonymous

Try sin² x = 1 - cos² x

10. anonymous

So the numerator becomes $1 - cos^2 x - 2 (sin x)(cos x) + cos^2 x$

11. Nnesha

that's right or just put 1 sin^2x+cos^2 =1 you will get the same answer :-)

12. anonymous

That is it peachpi.

13. anonymous

I did that a min ago and it did not work but re looked at it and I see where I made my mistake. Thank you all

14. anonymous

I think I over think these things at time. One minute I am rolling through them and then I get snagged by the simplest thing lol Thank you all

15. Nnesha

haha great work!!! :-)