# Homework Help: Solve this lim

1. Nov 6, 2009

### Dell

lim
x->pi/2 (1+cos2x)/cos3x

i tried all the identities and got

2cos^2(x)/cos(3x)

what now? i used cos(a+b)=cos(a)*cos(b)-sin(a)sin(b)
but no help there

2. Nov 6, 2009

### Dick

I don't think you tried 'all of the identities'. The denominator hasn't changed at all. What can you do to it?

3. Nov 7, 2009

### Dell

the best i could come up with is

lim
x->pi/2 (1+cos2x)/cos3x

lim
x->0 2cos^2(pi/2-x)/cos(3(pi/2-2))

lim
x->0 (2sin^2(x))/sin(3x)

lim
x->0 2sin(x)*-1/3

=0

Last edited: Nov 7, 2009
4. Nov 7, 2009

### lanedance

can you use L'hopitals? good to check with anyway...

5. Nov 7, 2009

### lanedance

EDIT: as below

in the mean time its worth trying Dick's suggestion though...

Last edited: Nov 7, 2009
6. Nov 7, 2009

### Dick

Ok, you can do it that way. cos(3(pi/2-x))=(-sin(3x)), though.

7. Nov 7, 2009

### Dick

I guess I was assuming the OP knew lim sin(x)/sin(3x)=(1/3) and didn't think sin(x)/sin(3x)=(1/3). Hope I wasn't wrong.

8. Nov 7, 2009