Question

find the value of 1-tan30/1+tan30​

Answer 1

2-✓3 is the answer_____

Step-by-step explanation:

$we \: know \: that \\ \boxed{ \frac{1 - tanØ}{1 +tanØ } = \tan( \frac{\pi}{4} - x) }$

$\frac{1 - tan30}{1 + tan30} = \tan( \frac{\pi}{4} - 30 )\\\boxed{tan(A-B)=\frac{tanA-tanB}{1-tanAtanB}} \\ \tan( \frac{\pi}{4} - 30)= \frac{tan(\frac{\pi}{4}) - tan30}{1 + tan \frac{\pi}{4} \times tan30 } \\ \\ = \frac{1 - \frac{1}{ \sqrt{3} } }{1 + \frac{1}{ \sqrt{3} } } \\\\ = \frac{ \frac{ \sqrt{3 } - 1}{ \sqrt{3} } }{ \frac{ \sqrt{3} + 1 }{ \sqrt{3} } }\\ \\ = \frac{ \sqrt{3 } - 1 }{ \sqrt{3} + 1 } \\\\ = \frac{ (\sqrt{3} - 1)( \sqrt{3} - 1) }{ (\sqrt{3} + 1)( \sqrt{3} - 1)} \\\\ =\frac{3-2\sqrt{3}+1}{3-1}\\\\=\frac{4-2\sqrt{3}}{2}\\\\=\frac{\cancel{2}(2-\sqrt{3})}{\cancel{2}}\\\\= 2-\sqrt{3}$