Question

show that tan75°+cot75°=4

Answer 1

tan75o = sqrt(3) + 1 / sqrt(3) - 1  

cot 75 = sqrt(3) - 1 / sqrt(3) + 1

on adding both of these we get

tan75 + cot75 = (sqrt(3) + 1)^2+(sqrt(3) - 1)^2  / (sqrt(3) - 1)(sqrt(3) + 1)

on solving you get answer 4