# I can't solve either of these.

3dsmax

## Homework Statement

1. DIRECTIONS: Use half-angle formulas to simplify the expression.

negative >>- *all square root*(1+cos4x/1-cos4x)

2. Verify the identity.

(sinx +/- siny)/(sinx + cosy) = Tan {(x +/- y)/(2)}

## Homework Equations

1. All half angle formulas.
2. Trig formulas. there is a bunch

## The Attempt at a Solution

1. i don't think its even possible
2. i don't see how this one is possible either

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cristo
Staff Emeritus
Have you really tried these?

1. $$- \sqrt{\frac{1+cos(4x)}{1-cos(4x)}}$$

What have you tried? What is the double angle formula for cos(4x) in terms of cos(2x), sin(2x)?

2.$$\frac{sinx \pm siny}{sinx+cosy}=tan\left(\frac{x \pm y}{2}\right)$$

Again, what have you tried? It might be easier to start with the right hand side, and write tan in terms of sin and cos, then work to the left.

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3dsmax
None of the half-angle formulas seemed to correspond to number 1. I tried using the half angle formula for number 2, but was thrown off by the "+/-" and don't know what to do.

cristo
Staff Emeritus
1. Make the substitution y=2x. Can you simplify cos(2y)?

2. Follow my hint, and write tan in terms of sin and cos. There are standard identities for $sin(A \pm B)$ and $cos(A \pm B)$. What identities do you know?

Show some work!

3dsmax
so like sin/cos (x +- y)/2

cristo
Staff Emeritus
You mean $$tan\left(\frac{x \pm y}{2}\right)=\frac{sin\left(\frac{x \pm y}{2}\right)}{cos\left(\frac{x \pm y}{2}\right)}$$

Now, do you know the identies I hinted at above?

3dsmax
They look like sum and difference identities. And how do you do that thing with the problem so that it looks good.

3dsmax
and how did you go from this:

https://www.physicsforums.com/latex_images/12/1241513-1.png [Broken]

to this:

https://www.physicsforums.com/latex_images/12/1241569-0.png [Broken]

It looks like part of sum to product but its not.

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cristo
Staff Emeritus
and how did you go from this:

https://www.physicsforums.com/latex_images/12/1241513-1.png [Broken]

to this:

https://www.physicsforums.com/latex_images/12/1241569-0.png [Broken]

It looks like part of sum to product but its not.
I didn't! Following my hint in post #2 I wrote tan in terms of sin and cos. Try and work from this to obtain the LHS of the identity.

I wrote my equations in LaTex; to see the code, click on the image.

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3dsmax
oh ok i see what you did you wrote what tan of that equals in sin over cosine and then that equals the left side. ok ok ok. now were on the same page i was confused. now........ hmm.....

so then do i now have to use these?

http://library.thinkquest.org/17119/media/3_501.gif

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cristo
Staff Emeritus
I would use the identities $\sin(A\pm B)=\sin A \cos B\pm \cos A\sin B$ and the corresponding identity for cosine, and let A = x/2 and B = y/2.

3dsmax
It just so happens that it doesn't really matter anyways. Cause my teacher said that this problems isn't possible to do anyway. Thanks for your time.

cristo
Staff Emeritus