Question

Prove that `(sqrt(3)+1)(3-cot30^@)=tan^3(60)^@-2sin60^@`

Answer 1

RHS= `tan^(3)60^(@)-2sin60^(@)=(sqrt(3))^(2) - 2sqrt(3)/2=3sqrt(3)-sqrt(3)=2sqrt(3)`
LHS`=(sqrt(3)+1)(3-cot30^(@))=(sqrt(3)+1)(3-sqrt(3))`
`therefore tan60^(2)=sqrt(3)sin60^(@)=sqrt(3)/2` and `=(sqrt(3)+1)sqrt(3)(sqrt(3)-1) cot 30^(@)=sqrt(3)`
`=sqrt(3)(sqrt(3))^(2)-1) = sqrt(3)(3-1)=2sqrt(3)`
`therefore` LHS = RHS Hence proved.