How do you simplify this ?

Question

# (tg15°)/(1-tg^2 15°) #

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Answer 1 · 2018-04-23T11:56:47

See below

#tan15=tan(45-30)#

Appliying formula #tan(a-b)=(tana-tanb)/(1+tanatanb)#

Then #tan15=tan(45-35)=(tan45-tan30)/(1+tan45tan30)=#

#=(1-sqrt3/3)/(1+sqrt3/3)=(3-sqrt3)/(3+sqrt3)=((3-sqrt3)(3-sqrt3))/(9-3)=(9-3sqrt3-3sqrt3+3)/6=(12-6sqrt3)/6=2-sqrt3#

#(2-sqrt3)^2=4-4sqrt3+3=7-4sqrt3#

Now in our formula

#tan15/(1-tan^2 15)=(2-sqrt3)/(1-7+4sqrt3)=(2-sqrt3)/(4sqrt3-6)=sqrt3/31#