Question

22. If cot theta - 1 / cot theta + 1 =1-√3 / 1+√3 then find the value of the acute angle theta

​

Answer 1

$\frac{cot \theta - 1}{cot \theta + 1} = \frac{1 - \sqrt{3} }{1 + \sqrt{3} } \\ using \: componendo \: dividedo \: method \\ \frac{(cot \theta - 1) + (cot \theta + 1)}{(cot \theta - 1) - (cot \theta + 1)} = \frac{(1 - \sqrt{3} ) + (1 + \sqrt{3} )} {(1 - \sqrt{3} ) - (1 + \sqrt{3}) } \\ : \implies \: \frac{2cot \theta}{ - 2} = \frac{2}{ - 2 \sqrt{3} } \\ :\implies \: cot \theta = \frac{1}{ \sqrt{3} } \\ : \implies \theta = \frac{\pi}{3} \: or \: 60 \degree$