2tan 50+tan 20=(tan 20+tan 50)+tan 50.....1

tan(50+20)=tan50+tan20/1-tan20.tan50

tan70(1-tan20.tan50)=tan50+tan20......2

now by comparing 1&2 we have 2tan 50+tan 20=tan70(1-tan20.tan50)+tan50

=tan70-tan20.tan50.tan70+tan50 as (tan70=cot20) we have

tan70-tan50+tan50=tan70