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

Question 565338: Evaluate and write radicals in simplest form using
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Evaluate and write radicals in simplest form tan( 300degrees - 45degrees ) using tan( alpha-beta ) = (tan(alpha) - tan (beta)) / (1+tan(alpha)* tan(beta))
**
let A=300�
let B=45�
tan(A-B)=(tanA-tanB)/1+tanA*tanB
..
tanA=tan 300�=-tan 60�=-√3 (in quadrant IV where tan<0)
tanB=tan 45�=1 (in quadrant I where tan>0)
..
tan(300-45)=(-√3-1)/1+(-√3*1)=(-√3-1)/(1-√3)=-(√3+1)/(1-√3)
tan(300�-45�)=-(√3+1)/(1-√3)
..
Check: Using calculator
tan(300-45)=tan(255�)≈3.732..
-(√3+1)/(1-√3)≈3.732..
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