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#(tan315 - tan30)/(1+tan315tan30)#

2 Answers
Abhishek K.
Mar 9, 2018

#(tan315-tan30)/(1+tan315tan30)=-(2+sqrt(3))#

Explanation:

#rarr(tan315-tan30)/(1+tan315tan30)#

#=tan(315-30)#

#=tan285#

#=tan(270+15)#

#=-cot15#

#=-1/tan15#

#=-1/tan(45-30)#

#=-1/((tan45-tan30)/(1+tan45tan30))#

#=(tan30+1)/(tan30-1)#

#=(1/sqrt3+1)/(1/sqrt3-1)#

#=(1+sqrt(3))/(1-sqrt(3))#

#=(1+sqrt(3))^2/(-2)=-(2+sqrt(3))#

maganbhai P.
Mar 9, 2018

#-2-sqrt(3)#

Explanation:

WE know that,
#tan(A-B)=(tanA-tanB)/(1+tanAtanB)#
So, #(tan315^0-tan30^0)/(1+tan315^0tan30^0)=tan(315^0-30^0)=tan285^0=tan(360^0-75^0)=-tan75^0=-2-sqrt3#
OR
#tan315^0=tan(270^0+45^0)=-tan45^0=-1andtan30^0=1/sqrt3#
so,
#(tan315^0-tan30^0)/(1+tan315^0tan30^0)=(-1-1/sqrt3)/(1-1*1/sqrt3)#
#=-((sqrt(3)+1)/(sqrt(3)-1))*((sqrt(3)+1)/(sqrt(3)-1))=-(3+2sqrt(3)+1)/(3-1)=-(4+2sqrt3)/2=-2-sqrt3#

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