document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972693>Question 972693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find cos(alpha - beta). Alpha and Beta are quadrant 1 angles with cos(alpha)=15/17 and csc(beta)=41/9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594953 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find cos(alpha - beta). Alpha and Beta are quadrant 1 angles with cos(alpha)=15/17 and csc(beta)=41/9<BR>\n" );
document.write( "***<BR>\n" );
document.write( "cos a=15/17<BR>\n" );
document.write( "sin a=&#8730;(1-cos^2(a))=&#8730;(1-225/289)=&#8730;(64/289)=8/17<BR>\n" );
document.write( "..<BR>\n" );
document.write( "csc b=41/9<BR>\n" );
document.write( "sin b=1/csc b=9/41<BR>\n" );
document.write( "cos b=&#8730;(1-sin^2(b))=&#8730;(1-81/1681)=&#8730;(1600/1681)=40/41<BR>\n" );
document.write( "...<BR>\n" );
document.write( "cos(a+b)=cos a cos b-sin a sin b=15/17*40/41-8/17*9/41=600/697-72/697=528/697<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "cos a=15/17<BR>\n" );
document.write( "a&#8776;28.07&#730;<BR>\n" );
document.write( "cos b=40/41<BR>\n" );
document.write( "b&#8776;12.68&#730;<BR>\n" );
document.write( "a+b&#8776;28.07+12.68<BR>\n" );
document.write( "a+b&#8776;40.75&#730;<BR>\n" );
document.write( "cos(a+b)&#8776;cos(40.75)&#8776;0.7575<BR>\n" );
document.write( "Exact value as computed=528/697&#8776;0.7575 </SPAN>\n" );
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