Question

Please answer the question​

Answer 1

Step-by-step explanation:

$1 + {cot}^{2} \theta \\ \\ = 1 + \dfrac{ {cos}^{2} \theta }{ {sin}^{2} \theta } \\ \\ = \dfrac{ {sin}^{2} \theta + {cos}^{2} \theta }{ {sin}^{2} \theta } \\ \\ = \dfrac{1}{ {sin}^{2} \theta } \\ \\ = {cosec}^{2} \theta \\ \bold{ \underline{formula \: used }}\longrightarrow \\ 1) tan \theta = \dfrac{sin \theta}{cos \theta} \\ 2)sin \theta = \dfrac{1}{cosec \theta}$

Answer 2

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