How do you simplify this ?

(tg15°)/(1-tg^2 15°)

1 Answer
Apr 23, 2018

See below

Explanation:

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