document.write( "Question 757903: If sin P=12/13 and cos Q=3/5 and both are acute angles,determine without the use of calculator the value of cos (P+Q) \n" ); document.write( "
Algebra.Com's Answer #461221 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
If sin P=12/13 and cos Q=3/5 and both are acute angles,determine without the use of calculator the value of cos (P+Q)
\n" ); document.write( "Identity: cos(P+Q)=cos P cos Q-sin P sin Q
\n" ); document.write( "..
\n" ); document.write( "given sin P=12/13
\n" ); document.write( "cos P=√(1-sin^2 P)
\n" ); document.write( "=√(1-(12/13)^2)
\n" ); document.write( "=√(1-144/169)
\n" ); document.write( "=√(25/169)
\n" ); document.write( "=5/13
\n" ); document.write( "..
\n" ); document.write( "given cos Q=3/5
\n" ); document.write( "sin Q=√(1-cos^2 Q)
\n" ); document.write( "=√(1-(3/5)^2)
\n" ); document.write( "=√(1-9/25)
\n" ); document.write( "=√(16/25)
\n" ); document.write( "=4/5
\n" ); document.write( "..
\n" ); document.write( "cos(P+Q)=cos P cos Q-sin P sin Q
\n" ); document.write( "=5/13*3/5-12/13*4/5
\n" ); document.write( "=15/65-48/65
\n" ); document.write( "=-33/65
\n" ); document.write( "..
\n" ); document.write( "Calculator check:
\n" ); document.write( "sin P=12/13
\n" ); document.write( "P≈67.38º
\n" ); document.write( "cos Q=3/5
\n" ); document.write( "Q≈53.13
\n" ); document.write( "P+Q≈67.38+53.13≈120.51º
\n" ); document.write( "cos(P+Q)≈cos(120.51)≈-0.5076..
\n" ); document.write( "exact value=-33/65≈-0.5076.. \n" ); document.write( "
\n" );