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## A dump of our free Chat sessions, in case it is useful. It excludes white boards used during paid sessions.

student : tan(210deg-45deg)
student : and can you show me why it comes out to sqrt3 -2?
tutorsd6 : tan ( 210 - 45 ) = tan 165 deg ( it is in the 2nd quadrant ) so it is negative
student : okay that makes sense, but i was trying to work through it by showing my work using the formula tan(a - b) = (tana - tanb) / 1 + tana*tanb
tutorsd6 : tan 210 = tan ( 180 + 30 ) = tan 30 = 1/ root 3
tutorsd6 : tan ( 210 - 45 ) = ( tan 30 - tan 45 ) / 1 + ( tan 30 * tan 45 )
student : yeah so (sqrt3/3 - 1) / 1 + sqrt3?
tutorsd6 : ( 1/sqrt3 - 1 ) / 1 + ( 1/sqrt 3 * 1 )
tutorsd6 : num : ( 1 - sqrt3 ) / sqrt 3
student : oh i thought tan30 = sqrt3/3
tutorsd6 : deno : sqrt 3 + 1
student : oh duh 1/sqrt3 is the same as sqrt3/3
student : ah im just confused at the part
( 1/sqrt3 - 1 ) / 1 + ( 1/sqrt 3 * 1 )
tutorsd6 : now understand ?
tutorsd6 : now just divide : num / deno
student : thats where i have my problems how does it get to 1 - sqrt3 ) / sqrt 3
student : do you have to multiply by a conjugate (excuse my spelling and my ignorance)
tutorsd6 : yes , you are correct
student : which would be if i may ask?
tutorsd6 : what you are asking ?
student : what is the conjugate, i have never really understood those
student : the conjugate that you would use
student : is the conjugate (1-(1/sqrt3))?

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