Question

cosxsin2x/1+cos2x
simplify

Answer 1

You probably mean:\[\frac{ \cos x \sin 2x }{ 1+\cos 2x }\]

To simplify, you need to apply the double-angle formulas:

sin2x=2sinxcosx
cos2x=1-2sin²x=2cos²x-1=cos²x-sin²x

Now can you honestly tell me you've learned these very important formulas by heart?

Answer 2

nope not yet i just started with these

Answer 3

OK, so learn them ;)

Now replace sin2x with 2sinxcosx and cos2x with one of the co2x identities. See if you can simplify after this.

Answer 4

2cos^2x= 1 + cos 2x---> numerator = 2cos^2x. denominator cosx *sin2x = 2sinxcosx . *cosx= 2cos^2x sinx . combine both to get sinx. is it help?

Answer 5

If I write it in the equation editor, it is much clearer for me:\[\frac{ \cos x 2\sin x \cos x }{ 1+2\cos^2x-1 }=\frac{ 2\sin x \cos^2x }{ 2\cos^2x }=\]I think you'll see where this is going to...

Answer 6

i have no idea of what the next step is

Answer 7

cancel out the same term from both sides

Answer 8

so then ill stay with sinx?

Answer 9

Yup!

Answer 10

thats my biggest problem.
idk how to do the correct steps.

Answer 11

Practising makes that (gradually) better, believe me!

Answer 12

Next time, chances are you can get one step further yourself...

Answer 13

Thank you for ur help, i'll post another one see if u can guide me through it

Answer 14

YW!