Question

if cosec theta+cot theta=p find the value of sin theta

Answer 1

Here is the answer it may help you

Answer 2

given

$cosec \theta + cot \theta = p$

we know

${cosec}^{2} \theta - {cot}^{2} \theta = 1$

so

$p(cosec \theta - cot \theta) = 1 \\ \\ cosec \theta - cot \theta = \frac{1}{p}$

Now adding this two values

$cosec \theta + cot \theta + cosec \theta - cot \theta = p + \frac{1}{p} \\ \\ 2cosec \theta = \frac{ {p}^{2} + 1 }{p} \\ \\ cosec \theta = \frac{ {p}^{2} + 1}{2p} \\ \\ sin \theta = \frac{2p}{ {p}^{2} + 1}$