Simplifying Trigonometric Problems | Proven Equations & Solutions

[imbroglio]

Homework Statement

Simplify
The problem is either 1+[(cosx)/2]
or
1+[cos (x/2)]

The first one looks unworkable so I'm going with the second...unless any of you see that the first one looks normal...

Homework Equations

I derived/proved some below...

The Attempt at a Solution

1+cos(x/2)
cos^2x=2cos(x/2)-1
cos(x/2)= sqrt [(cos^2x+1)/2]

(1+sqrt [(cos^2x+1)/2])^2

[1+cos^2x+1]/2

(2+cos^2x)/2

[2+cos^2x]/2

[(1-2sin^2x)+2]/2

(1/2)-sin^2x

and now I'm obviously stuck...
Thanks for all your help!

 

[Gib Z]

What are you trying to get it to? Simplify can mean a lot of different things when dealing with trig.

 

[HallsofIvy]

Homework Statement

Simplify
The problem is either 1+[(cosx)/2]
or
1+[cos (x/2)]

The first one looks unworkable so I'm going with the second...unless any of you see that the first one looks normal...

Those are expressions, not "problems". What do you want to do with them? And what do you mean by "is either"? Do you get to choose?

Homework Equations

I derived/proved some below...

The Attempt at a Solution

1+cos(x/2)
cos^2x=2cos(x/2)-1

No, this is clearly untrue when $x= \pi/2$, for example. Perhaps you were thinking of cos(2x)= 2 cos²(x)- 1

cos(x/2)= sqrt [(cos^2x+1)/2

No, $cos(x/2)= \sqrt{(cos(x)+ 1)/2}$

(1+sqrt [(cos^2x+1)/2])^2

[1+cos^2x+1]/2

(2+cos^2x)/2

[2+cos^2x]/2

[(1-2sin^2x)+2]/2

(1/2)-sin^2x

and now I'm obviously stuck...
Thanks for all your help!

Again, what are you trying to do? If the problem is to simplify either 1+ (cos(x))/2 or 1+ cos(x/2), they both look like they are already about as simple as you are going to make them!

 

[imbroglio]

Sorry for all of the confusion.

Simplify simply means to change the form of the problem to a more "simplified state"...in my class any how.

As you can see I am quite elementary in my trigonometry...however I did manage to simplify the problem...when I have my work with me I might post how I finally finished it.

Thank you for everything and your time, although I am sorry that it took time and that it was impossible for you to help me because my mathematical errors.

Your insight is fantastic. Have a fantastic evening.