Question

show that

Answer 1

\[\huge\tan 7^{0}30 '=\sqrt{6}+\sqrt{2}-\sqrt{3}-2\]

Answer 2

what is this \['\] notation

Answer 3

the single ' means arc minutes, usually just called minutes, meaning 1/60 of a degree
See http://zonalandeducation.com/mmts/trigonometryRealms/degMinSec/degMinSec.htm

30' means 30/60 of a degree or 0.5 degrees
7º 30' = 7.5º

Answer 4

tan(7.5) =tan(15/2)
tan(15)=tan(30/2)
tan(30)=1/root3

Answer 5

This should help
tanx=2tan(x/2) /(1-tan^2(x/2) )
So,