How can you prove that Tan 75° + cot 75°=4?

tan75°

 = tan(45°+30°) 

= (tan45° + tan30°) /( 1 - tan45° tan30°)

=(1+ (1/√3)) / ( 1 - (1)(1/√3)) 

= (√3+1) / (√3–1) 

on rationalising the denominator

= (1+√3)² /2 = (1+3+2√3) / 2 = 2 + √3

Cot 75° = 1 / Tan75° = 1 /(2 + √3) = (2 - √3) / (4–3)=2 - √3

Tan75° + cot75° = 2 + √3 + 2 - √3 = 4

another  proof tan 75 + cot 75 = 4 click here