1.

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Answer»

LHS:(tan60°+1/tan60°-1)^2 =[(√3+1)/(√3-1)]^2=[(√3+1)(√3+1)/(√3-1)(√3+1)]^2=[(3+2√3+1)/(3-1)]^2=[(4+2√3)/2]^2 =[2(2+√3)/2]^2 =(2+√3)^2= 4 + 4√3 + 3= 7 + 4√3

RHS:(1 + cos30°)/(1 - cos30°)= (1 + cos30)^2/(1 - cos^2 30)= (1 + cos 30)^2/sin^2 30= (1 + cos^2 30 + 2cos30)/ sin^2 30= (1 + 3/4 + √3) /(1/4)= [(7 + 4√3)/4]/(1/4)= 7 + 4√3

LHS = RHS

Hence proved



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