Question

1+ cot theta= cosec theta general value of theta​

Answer 1

Answer:

$general \: value \: of \: \theta \\ \theta = n \: \pi + \frac{\pi}{2}$

Step-by-step explanation:

To find the general solution of the equation

$1 + cot \: \theta = cosec \: \theta \\ we \: know \: that \\ \\ 1 + {cot}^{2} \theta = {cosec}^{2} \theta \\ \\ so \\ \: cosec \: \theta = \sqrt{1 + {cot}^{2} \theta } \\ \\ apply \: to \: the \: equation \\ \\ 1 + cot \: \theta = \sqrt{1 + {cot}^{2} \theta } \\ \\ squaring \: both \: side \\ \\ {(1 + cot \: \theta)}^{2} = ({\sqrt{1 + {cot}^{2} \theta }})^{2} \\ \\ 1 + {cot}^{2} \theta + 2cot \: \theta = 1 + {cot}^{2} \theta \\ \\ 2cot \: \theta = 0 \\ \\ cot \: \theta = 0 \\ \\ tan\: \theta = not \: defined \\ \\ tan \: \theta = tan \: 90 \\ \\ \theta = n \: \pi + \frac{\pi}{2}$

Hope it helps you.