Please help me prove this identity!

[gabespeep]

I need to prove the following identity.

1-cos(2t)/cos(t)sin(t)=2tan(t)

So far this is what I have but my left side does not equal my right side.

1-cos(2t)/cos(t)sin(t)
=1-1-2sin^2(t)/cos(t)sin(t)
=-2sin^2(t)/cos(t)sin(t)
=-2sin(t)/cos(t)
=-2tan(t)?

I used the double angle identity for cos(2t) and I am pretty sure after that is where I am making my mistake. Maybe I am making the problem harder then it is? Any help or guidence in the right direction would be much appreciated!

 

[Deleted member 4993]

I need to prove the following identity.

1-cos(2t)/cos(t)sin(t)=2tan(t)

So far this is what I have but my left side does not equal my right side.

[1-cos(2t)]/[cos(t)sin(t)]

=[1-{1-2sin^2(t)}]/[cos(t)sin(t)]

= 2sin^2(t)/[cos(t)sin(t)]

= 2sin(t)/cos(t)

= 2tan(t)

I used the double angle identity for cos(2t) and I am pretty sure after that is where I am making my mistake. Maybe I am making the problem harder then it is? Any help or guidence in the right direction would be much appreciated!

Your mistake is:

not using proper grouping symbols → sloppy work

 

[gabespeep]

Thanks for the help!

Thank you for telling me where I went wrong, and correcting my grouping symbols so that my answer came out like it should. I agree not using symbols properly makes all the math very sloppy and I will keep that in mind from this point on. Once again thank you for taking the time to show me where I was incorrect.