`LHS=(2tan^(2)30^(@))/(1-tan^(2)30^(@))+sec^(2)45^(@)-cot^(2)45^(@)`
`=(2xx((1)/(sqrt(3)))^(2))/(1-((1)/(sqrt(3)))^(2))+(sqrt(2))^(2)-(1)^(2) =(2xx(1)/(3))/(1-(1)/(3))+2-1=((2)/(3))/((2)/(3)) +1=1+1=2`
`RHS=sec60^(@)=2`
`therefore LHS= RHS`. [Proved]