Question 473053
<pre><b>
sin<font face="symbol">q</font> = cos(<font face="symbol">q</font> - 30°)

The word "<font color="red">co</font><font color="green">sine</font>" is an abbreviation for "<font color="red">co</font>mplement's <font color="green">sine</font>"

If the sine of one positive acute angle equals the
cosine of another positive acute angle, then the
angles are complementary.  Therefore:

<font face="symbol">q</font> + (<font face="symbol">q</font> - 30°) = 90°

  <font face="symbol">q</font> + <font face="symbol">q</font> - 30° = 90°
    
     2<font face="symbol">q</font> - 30° = 90°
 
           2<font face="symbol">q</font> = 120°

            <font face="symbol">q</font> = 60°  

sin<font face="symbol">q</font> = {{{sqrt(3)/2}}}

cos<font face="symbol">q</font> = {{{1/2}}}

sin<font face="symbol">q</font> + cos<font face="symbol">q</font> = {{{(1+sqrt(3))/2}}}.

Edwin</pre>