Question 1181125
.


            The numbers and calculations in the post by @mananth are INCORRECT.


            Therefore, for your safety,  IGNORE  his  (or her)  post.


            I came to bring a correct solution.




<pre>
cos A = {{{3/5}}},  A is in Quadrant 1 

sin A = {{{sqrt(1-cos^2(A))}}} = {{{sqrt(1-(3/5)^2)}}} = {{{sqrt(1-(9/25))}}} = {{{sqrt(16/25))}}} = {{{4/5}}}, 

cos A = {{{3/5}}}, tan A = {{{4/3}}}


tan B = {{{12/5}}}, quadrant III   ( ! not quadrant IV, as @mananth mistakenly wrote ! )

tan B = {{{12/5}}}, sin B = {{{-12/13}}}, cos B = {{{-5/13}}}


sin (A + B) = sin(A)cos(B) + cos(A)sin(B) = {{{(4/5)(-5/13)}}} + {{{(3/5)(-12/13)}}} = {{{-20/65}}} - {{{36/65}}} = {{{-56/65}}}.


sin(A − B) = sin(A)*cos(B) − cos(A)*sin(B) = {{{(4/5)(-5/13)}}} - {{{(3/5)(-12/13)}}} = {{{-20/65}}} + {{{36/65}}} = {{{16/65}}}.


cos(A + B) = cos A cos B − sin A sin B 
cos(A − B) = cos A cos B + sin A sin B 
sin(A + B) = sin A cos B + cos A sin B 


Plug values and continue
</pre>

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To see many other similar solved problems on calculating trig functions, &nbsp;look into the lessons  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Calculating-trigonometric-functions-of-angles.lesson>Calculating trigonometric functions of angles</A>

&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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Evaluating-trigonometric-expressions.lesson>Evaluating trigonometric expressions</A> 

in this site.


Also, &nbsp;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 lessons are the part of this online textbook under the topic &nbsp;"<U>Trigonometry: Solved problems</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.