document.write( "Question 754852: Given that A and B are acute and Sin A = 4/5, Cos B = 7/25. Find wihout using table the value of tan (A - B). \n" ); document.write( "

Algebra.Com's Answer #459356 by lwsshak3(11628) $\"\"$ $\"About$

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Given that A and B are acute and Sin A = 4/5, Cos B = 7/25. Find wihout using table the value of tan (A - B).
\n" ); document.write( "***
\n" ); document.write( "Identity: $\"tan%28A-B%29=%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29+tan%28B%29%29\"$
\n" ); document.write( "sinA=4/5
\n" ); document.write( "working with a 3-4-5 right triangle in Q1
\n" ); document.write( "tanA=opposite side/adjacent side=4/3
\n" ); document.write( "..
\n" ); document.write( "cosB=7/25
\n" ); document.write( "opposite side=√(25^2-7^2)=√576=24
\n" ); document.write( "tanB=opposite side/adjacent side=24/7
\n" ); document.write( "..
\n" ); document.write( " $\"tan%28A-B%29=%284%2F3-24%2F7%29%2F%281%2B4%2F3%2A24%2F7%29\"$
\n" ); document.write( " $\"tan%28A-B%29=%2828%2F21-72%2F21%29%2F%281%2B96%2F21%29\"$
\n" ); document.write( " $\"tan%28A-B%29=%28-44%2F21%29%2F%28117%2F21%29\"$
\n" ); document.write( " $\"tan%28A-B%29=+-44%2F117\"$
\n" ); document.write( "..
\n" ); document.write( "Check with calculator:
\n" ); document.write( "sinA=4/5
\n" ); document.write( "A≈53.13º
\n" ); document.write( "cosB=7/25
\n" ); document.write( "B≈73.74º
\n" ); document.write( "A-B≈-20.61º
\n" ); document.write( "tan(A-B)=tan(-20.61º)≈-0.3760..
\n" ); document.write( "Exact value=-44/117≈-0.3760.. \n" ); document.write( "

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