MHB Possible Miscalculation on Identity-Completion

[Dundee3]

Hey homies, I've been working on some of my usual jazz, when I came across one hiccup.

My problem is this:

sin(5x)sin(8x)cos(5x)cos(8x)

x = theta, and my objective is to complete the identity.According to my notes, the correct solution is:

[cos^2(3x) - cos^2(13x)] / 4I just can't bring my own solution to match the one that has been given.Any help would be totally cool.

Thanks guys, Merry Christmas <3

 

[SuperSonic4]

Hey homies, I've been working on some of my usual jazz, when I came across one hiccup.

My problem is this:

sin(5x)sin(8x)cos(5x)cos(8x)

x = theta, and my objective is to complete the identity.According to my notes, the correct solution is:

[cos^2(3x) - cos^2(13x)] / 4I just can't bring my own solution to match the one that has been given.Any help would be totally cool.

Thanks guys, Merry Christmas <3

What have you tried? You may want to use the following identities

$$\cos(A)\cos(B) = \dfrac{\cos(A-B) + \cos(A+B)}{2}$$

$$\sin(A)\sin(B) = \dfrac{\cos(A-B) - \cos(A+B)}{2}$$

 

[Dundee3]

Nailed it.Would it be presumptuous to ask for help on another?

 

[MarkFL]

Nailed it.Would it be presumptuous to ask for help on another?

You are free to ask for help on other questions, we just ask that you begin a new thread for each new question, and to show what you have tried in each case. This way our helpers have a better understanding of where you need help exactly and can give more specific suggestions.

 

[Dundee3]

Superb. I'll create the new thread shortly, and I will be happy to post the solution for the last problem that involves my work. For future posts, I was wondering if there was a certain trick to activate the 'Latex' text-formatting so that I may enter more legible characters into my posts? I've tried in the past, but I've failed every time and just resorted to using standard ASCII characters.

I'll attempt to post the solution to the previous problem here as an example:

\sin\left({5}\right)\sin\left({8}\right)\cos\left({5}\right)\cos\left({8}\right)=

1/2[cos(5\theta-8\theta)-cos(5\theta+8\theta)]1/2[cos(5\theta-8\theta)+cos(5\theta + 8\theta)]

1/4[cos3\theta - cos13\theta][cos3\theta + cos13\theta]

1/4[cos^23\theta - cos^2 13\theta]

 

[MarkFL]

Superb. I'll create the new thread shortly, and I will be happy to post the solution for the last problem that involves my work. For future posts, I was wondering if there was a certain trick to activate the 'Latex' text-formatting so that I may enter more legible characters into my posts? I've tried in the past, but I've failed every time and just resorted to using standard ASCII characters.

I'll attempt to post the solution to the previous problem here as an example:

\sin\left({5}\right)\sin\left({8}\right)\cos\left({5}\right)\cos\left({8}\right)=

1/2[cos(5\theta-8\theta)-cos(5\theta+8\theta)]1/2[cos(5\theta-8\theta)+cos(5\theta + 8\theta)]

1/4[cos3\theta - cos13\theta][cos3\theta + cos13\theta]

1/4[cos^23\theta - cos^2 13\theta]

What you need to do is enclose your $\LaTeX$ code within tags...I recommend using our MATH tags, which you can easily generate by clicking the $\sum$ button on our toolbar. Click this button, and the opening and closing tags are generated, with the cursor then conveniently located between them ready for you to enter your code. You may also first enter your code, then select it, and then click the button on the toolbar, and your selected text will be wrapped with the tags.

For example the code:

$$\sin^2(\theta)+\cos^2(\theta)=1$$

produces:

$$\sin^2(\theta)+\cos^2(\theta)=1$$

 

[Dundee3]

$$\sin5\theta\sin8\theta\cos5\theta\cos8\theta=$$$$\frac{1}{2}[\cos(5\theta - 8\theta) - \cos(5\theta+8\theta]1/2[cos(5\theta-8\theta)+cos(5\theta + 8\theta)]$$

$$\frac{1}{4}[\cos3\theta - \cos13\theta][\cos3\theta + \cos13\theta]$$

$$\frac{1}{4}[\cos^2(3\theta) - \cos^2(13\theta)]$$

That's my solution =)

Thank you so much man =)

 

[MarkFL]

To write fractions in a vertical format, use the code:

\frac{numerator}{denominator}

For example, the code:

$$\frac{x}{y}$$

Generates:

$$\frac{x}{y}$$

I would encourage you to look at our Quick $\LaTeX$ element on our posting pages to generate the codes you may need for various mathematical forms. Pretty much anything you will need can be found there. Clicking the symbols on that element will generate the code you need at your current cursor location. :D

 

[Dundee3]

Edited! We've spent some time together today, Mate. Have a good one! I actually have an exam later, so this will really help. You're a life-saver.

 

[Greg]

If you haven't thought of it already, clicking on "Reply With Quote" and examining the code there is a handy way of investigating LaTeX code that you are curious about. :)