Question

The value of Tan 75º- cot 75º =​

Answer 1

$\tan(45 + 30) - \cot(45 + 30) \\ \\ = > \frac{ \tan45 + \tan30}{1 - \tan45 \tan30} - \frac{ \cot45 \cot30 - 1}{ \cot30 + \cot45} \\ \\ = > \frac{1 + \frac{1}{ \sqrt{3} } }{1 - 1 \times \frac{1}{ \sqrt{3} } } - \frac{1 \times \sqrt{3} - 1}{ \sqrt{3} + 1 } \\ \\ = > \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } - \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \\ \\ = > \frac{ {( \sqrt{3} + 1) }^{2} - {( \sqrt{3} - 1) }^{2} }{3 - 1} \\ \\ = > \frac{3 + 1 + 2 \sqrt{3} - 3 - 1 + 2 \sqrt{3} }{2} \\ \\ = > \frac{4 \sqrt{3} }{2} = 2 \sqrt{3}$