Question

Find the value of 1-cot²75

Answer 1

$1 - co {t}^{2} 75 \\ = 1 - (2 - \sqrt{3} { \: )}^{2} \\ = 1 - (4 + 3 - 4 \sqrt{3} ) \\ = 1 - (7 - 4 \sqrt{3} ) \\ = 1 - 7 + 4 \sqrt{3} \\ = 4 \sqrt{3} - 6 \\ = 2(2 \sqrt{3} - 3)$

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