# Thread: trigo problem no. 23

1. ## trigo problem no. 23

trigo problem no. 23
p213 q14
Thanks

2. I think the important word you are missing is "suitable". You should have THREE double-angle formulas for cosine.

$\displaystyle \cos(2\theta)\;=\;2\cos^{2}(\theta)-1\;=\;1-2\sin^{2}(\theta)\;=\;\cos^{2}(\theta)-\sin^{2}(\theta)$

I believe you will find the last most "suitable" for your conditions. It factors as a difference of squares and should be obvious from there.

3. that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!

4. Originally Posted by afeasfaerw23231233
that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!
It is a quite useful hint. In fact, I think it's rather clever.
$\displaystyle cos(2\theta) = sin(\theta) + cos(\theta)$

Now use the hint: $\displaystyle cos(2\theta) = cos^2(\theta) - sin^2(\theta)$

$\displaystyle cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)$

Now factor the left hand side and see what comes of it.

-Dan

5. Originally Posted by topsquark
It is a quite useful hint. In fact, I think it's rather clever.
$\displaystyle cos(2\theta) = sin(\theta) + cos(\theta)$

Now use the hint: $\displaystyle cos(2\theta) = cos^2(\theta) - sin^2(\theta)$

$\displaystyle cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)$

Now factor the left hand side and see what comes of it.

-Dan
thank you for your help! why i thought of it for such a long time but couldn't see it. thanks again.
EDIT: ah.. TKhunny already gave the hint to me but i was in a hurry and didn't see it. how stupid i am....

6. Originally Posted by afeasfaerw23231233
thank you for your help! why i thought of it for such a long time but couldn't see it. thanks again.
EDIT: ah.. TKhunny already gave the hint to me but i was in a hurry and didn't see it. how stupid i am....
Not stupid...you've just not had enough experience at it. This is how you get experience.

-Dan

7. Let's put a couple of things on your list of things to learn:

1) Have a little patience with yourself. No sense beating yourself up. Not everything is easy.

2) Just a little LaTeX can go a long way. It takes up WAY less space than scanned images.

Good deal. What else are you working on?