Prove that tan75 + cot75 = 4

tan75^o = 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

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Approved

tan75°=tan(30°+45°)

=(tan30°+tan45°)/(1-tan30°tan45°)

={(1/√3)+1}/{1-(1/√3)(1)}

=(√3+1)/(√3-1)

So,cot75°=1/tan75°

=(√3-1)/(√3+1)

Then,tan75°+cot75°={(√3+1)²+(√3-1)²}/{(√3)²-(1)²}

=(3+1+2√3+3+1-2√3)/(3-1)

=4.

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The value of tan 75°=2-root3It`s very easy and simple just the thing is you have to remember the formula. I will say you in a easy and simple methodThe value of cot 75°=2+root3Tan75°+cot75°2-root3+2+root3=4I hope you got the answer