Question

If cos theta-sin theta /cos theta +sin theta=1-root 3+1+rot 3 . Find theta

Answer 1

$\frac{cos \theta - sin \theta}{cos \theta + sin \theta} = \frac{1 - \sqrt{3} }{1 + \sqrt{3} } \\ \\ using \: componendo \: dividendo \\ \\ \frac{(cos \theta - sin \theta) + (cos \theta + sin \theta)}{(cos \theta - sin \theta) - (cos \theta + sin \theta)} = \frac{1 - \sqrt{3} + 1 + \sqrt{3} }{1 - \sqrt{3} - 1 - \sqrt{3} } \\ \\ \frac{2cos \theta}{ - 2sin \theta} = \frac{2}{ - 2 \sqrt{3} } \\ \\ cot \theta = \frac{1}{ \sqrt{3} } \\ \\ \theta = 60 \degree \: \: \: or \: \: \frac{\pi}{3}$