Question 1051560
.
<pre>
= {{{sin(alpha)*cos(beta) - cos(alpha)*sin(beta)}}} = 

= {{{(12/13)*(12/13) - (5/13)*(5/13)}}} = {{{(144-25)/169}}} = {{{119/169}}}.
</pre>

For details, see the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Selected-problems-from-the-archive-on-calculating-trig-functions-of-angles.lesson>Advanced problems on calculating trigonometric functions of angles</A>, Problem 1

in this site.


You will find there the detailed solution of the similar problem.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Trigonometry: Solved problems</U>".


You will find many other closely related problems under this topic.