document.write( "Question 565338: Evaluate and write radicals in simplest form $\"+tan%28+300degrees+-+45degrees+%29+\"$ using \n" ); document.write( "

Algebra.Com's Answer #365755 by lwsshak3(11628) $\"\"$ $\"About$

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Evaluate and write radicals in simplest form tan( 300degrees - 45degrees ) using tan( alpha-beta ) = (tan(alpha) - tan (beta)) / (1+tan(alpha)* tan(beta))
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\n" ); document.write( "let A=300º
\n" ); document.write( "let B=45º
\n" ); document.write( "tan(A-B)=(tanA-tanB)/1+tanA*tanB
\n" ); document.write( "..
\n" ); document.write( "tanA=tan 300º=-tan 60º=-√3 (in quadrant IV where tan<0)
\n" ); document.write( "tanB=tan 45º=1 (in quadrant I where tan>0)
\n" ); document.write( "..
\n" ); document.write( "tan(300-45)=(-√3-1)/1+(-√3*1)=(-√3-1)/(1-√3)=-(√3+1)/(1-√3)
\n" ); document.write( "tan(300º-45º)=-(√3+1)/(1-√3)
\n" ); document.write( "..
\n" ); document.write( "Check: Using calculator
\n" ); document.write( "tan(300-45)=tan(255º)≈3.732..
\n" ); document.write( "-(√3+1)/(1-√3)≈3.732.. \n" ); document.write( "

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