document.write( "Question 960793: find exact value of a) sin(alpha+beta); b) cos(alpha+beta); c) tan(alpha-beta) given that cos(alpha)=radical 5/5 5 in Q1 & sin(beta)= -4/5 in Q4 \n" ); document.write( "
Algebra.Com's Answer #587169 by stanbon(75887)\"\" \"About 
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find exact value of
\n" ); document.write( "a) sin(alpha+beta)
\n" ); document.write( "b) cos(alpha+beta)
\n" ); document.write( "c) tan(alpha-beta)
\n" ); document.write( "given that cos(alpha)=sqrt(5)/5 in Q1 & sin(beta)= -4/5 in Q4
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\n" ); document.write( "If cos(a) = sqrt(5)/5 , sin(a) = sqrt(5^2-5)/5 = sqrt(20)/5 = (2sqrt(5)/5
\n" ); document.write( "Then tan(a) = sin(a)/cos(a) = [2sqrt(5)/5]/[sqrt(5)/5] = 2
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\n" ); document.write( "If sin(b) = -4/5 in QIV, cos(b) = sqrt(5^2-4^2)/5 = 3/5
\n" ); document.write( "Then tan(b) = sin(b)/cos(b) = (-4/5)/(3/5) = -4/3
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\n" ); document.write( "a) sin(a+b)=sin(a)cos(b)+cos(a)sin(b)=(2sqrt(5)/5)*(3/5)+(sqrt(5)/5)*(-4/5)
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\n" ); document.write( "= (6sqrt(5)/25)-4sqrt(5)/25 = 2sqrt(5)/25
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\n" ); document.write( "Comment:: For b) and c) fill in the values to get the answers::
\n" ); document.write( "b) cos(a+b) = cos(a)cos(b)-sin(a)sin(b)
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\n" ); document.write( "c) tan(a-b) = [tan(a)-tan(b)]/[1+tan(a)*tan(b)]
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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