L.H.S: (√3 + 1) (3 – Cot30°)
![\[=\text{ }\left( \surd 3\text{ }+\text{ }1 \right)\text{ }\left( 3\text{ }\text{ }\surd 3 \right)\text{ }\left[ \because cos\text{ }30{}^\circ =\surd 3 \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a99618c0b35779f1a54a8aa20650a162_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( \surd 3\text{ }+\text{ }1 \right)\text{ }\left( \surd 3\text{ }\text{ }1 \right)\text{ }\left[ \because \left( 3\surd 3 \right)\text{ }=\text{ }\left( \surd 31 \right) \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d3bf137e9265bd7bf39c049d8e54b012_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( \left( \surd 3 \right)21 \right)\text{ }\surd 3\text{ }\left[ \because \left( \surd 3+1 \right)\left( \surd 3-1 \right)\text{ }=\text{ }\left( \left( \surd 3 \right)21 \right) \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2a1d9caf807653c6c8635cb3486d4948_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( 3-1 \right)\text{ }\surd 3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6bdb732c52712b4e3c52924d4f3e6325_l3.png "Rendered by QuickLaTeX.com")
= 2√3
Also settling R.H.S: tan3 60° – 2 sin 60°
Since, tan 60o = √3 and sin 60o = √3/2,
We get,
![\[\left( \surd 3 \right)3\text{ }\text{ }2.\left( \surd 3/2 \right)\text{ }=\text{ }3\surd 3\text{ }\text{ }\surd 3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3eafaeac3bc8b715ad752b404b6f00e2_l3.png "Rendered by QuickLaTeX.com")
= 2√3
Along these lines, L.H.S = R.H.S
Thus, demonstrated.
(√3+1) (3 – cot 30°) = tan3 60° – 2 sin 60°
(√3+1) (3 – cot 30°) = tan3 60° – 2 sin 60°