2011/080) prove that Tan 55 = tan35+ 2tan20

20 = 55 - 35

take tan of both sides

tan 20 = (tan 55 - tan 35)/(1+ tan 55 tan 35)

but as 55 + 35 = 90 so tan 35 = cot(90-35) = cot 55

so tan 20 = (tan 55 - tan 35)/(1+ tan 55 tan 35) = tan 20 = (tan 55 - tan 35)/(1+ tan 55 cot 55)
= (tan 55 - tan 35)/(1+ 1) = (tan 55 - tan 35)/2
or 2 tan 20 = tan 55 - tan 35

or tan 55 = tan 35 + 2 tan 20