SOLUTION: Evaluate and write radicals in simplest form {{{ tan( 300degrees - 45degrees ) }}} using {{{ tan( alpha-beta ) = (tan(alpha) - tan (beta)) / (1+tan(alpha)* tan(beta)) }}}

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate and write radicals in simplest form {{{ tan( 300degrees - 45degrees ) }}} using {{{ tan( alpha-beta ) = (tan(alpha) - tan (beta)) / (1+tan(alpha)* tan(beta)) }}}      Log On


   

Question 565338: Evaluate and write radicals in simplest form +tan%28+300degrees+-+45degrees+%29+ using
Answer by lwsshak3(11628) About Me  (Show Source):
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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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let A=300º
let B=45º
tan(A-B)=(tanA-tanB)/1+tanA*tanB
..
tanA=tan 300º=-tan 60º=-√3 (in quadrant IV where tan<0)
tanB=tan 45º=1 (in quadrant I where tan>0)
..
tan(300-45)=(-√3-1)/1+(-√3*1)=(-√3-1)/(1-√3)=-(√3+1)/(1-√3)
tan(300º-45º)=-(√3+1)/(1-√3)
..
Check: Using calculator
tan(300-45)=tan(255º)≈3.732..
-(√3+1)/(1-√3)≈3.732..