L.H.S: (√3 + 1) (3 – Cot30°)

\[=\text{ }\left( \surd 3\text{ }+\text{ }1 \right)\text{ }\left( 3\text{ }\text{ }\surd 3 \right)\text{ }\left[ \because cos\text{ }30{}^\circ =\surd 3 \right]\]

\[=\text{ }\left( \surd 3\text{ }+\text{ }1 \right)\text{ }\left( \surd 3\text{ }\text{ }1 \right)\text{ }\left[ \because \left( 3\surd 3 \right)\text{ }=\text{ }\left( \surd 31 \right) \right]\]

\[=\text{ }\left( \left( \surd 3 \right)21 \right)\text{ }\surd 3\text{ }\left[ \because \left( \surd 3+1 \right)\left( \surd 3-1 \right)\text{ }=\text{ }\left( \left( \surd 3 \right)21 \right) \right]\]

\[=\text{ }\left( 3-1 \right)\text{ }\surd 3\]

= 2√3

Also settling R.H.S: tan3 60° – 2 sin 60°

Since, tan 60o = √3 and sin 60o = √3/2,

We get,

\[\left( \surd 3 \right)3\text{ }\text{ }2.\left( \surd 3/2 \right)\text{ }=\text{ }3\surd 3\text{ }\text{ }\surd 3\]

= 2√3

Along these lines, L.H.S = R.H.S

Thus, demonstrated.