Question 565338
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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let A=300º
let B=45º
tan(A-B)=(tanA-tanB)/1+tanA*tanB
..
tanA=tan 300º=-tan 60º=-&#8730;3 (in quadrant IV where tan<0)
tanB=tan 45º=1 (in quadrant I where tan>0)
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tan(300-45)=(-&#8730;3-1)/1+(-&#8730;3*1)=(-&#8730;3-1)/(1-&#8730;3)=-(&#8730;3+1)/(1-&#8730;3)
tan(300º-45º)=-(&#8730;3+1)/(1-&#8730;3)
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Check: Using calculator
tan(300-45)=tan(255º)&#8776;3.732..
-(&#8730;3+1)/(1-&#8730;3)&#8776;3.732..