Question 1143417
.


            In this post,  my goal is to present the solution in more compact form comparing with the Edwin's post.



<pre>
1.  Since sin(B) = {{{-1/2}}}  and since B is the angle in QIV, where cosine is positive, we have

        cos(B) = {{{sqrt(1-sin^2(B))}}} = {{{sqrt(1-1/4)}}} = {{{sqrt(3/4)}}} = {{{sqrt(3)/2}}};

        hence,  tan(B) = {{{sin(B)/cos(B)}}} = {{{((-1/2))/((sqrt(3)/2))}}} = {{{-1/sqrt(3)}}}.



2.  Since sin(C) = {{{1/4}}}  and since C is the angle in QII, where cosine is negative, we have

        cos(C) = {{{-sqrt(1-sin^2(C))}}} = {{{-sqrt(1-1/16)}}} = {{{-sqrt(15/16)}}} = {{{-sqrt(15)/4}}};

        hence,  tan(C) = {{{sin(C)/cos(C)}}} = {{{-((1/4))/((sqrt(5)/4))}}} = {{{-1/sqrt(5)}}}.



3.  Now apply the formula for tangent of sum

        tan(B+C) = {{{(tan(B) + tan(c))/(1 - tan(B)*tan(C))}}} = {{{(-1/sqrt(3) - 1/sqrt(5))/(1 - (-1/sqrt(3))*(-1/sqrt(5)))}}}.


     At this point, we have the same formula as Edwin has in his post, and further simplifications can be done by the same way as Edwin did. 
</pre>

You can see many other similar problems solved in my 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.