Question

When each term of sin? 0 + cos2 0 = 1 is divided by sin²0, what will be the
result?​

Answer 1

${sin}^{2} x + {cos}^{2} x = 1 \\ \\ dividing \: throughout \: by \: {sin}^{2} x \\ \\ \frac{ {sin}^{2} x}{ {sin}^{2} x} + \frac{ {cos}^{2} x}{ {sin}^{2}x } = \frac{1}{ {sin}^{2}x } \\ 1 + {cot}^{2} x = {cosec}^{2} x \: \: \: \: ... \binom{ \frac{cosx}{sinx} = cotx}{ \frac{1}{sinx} = cosecx }$

Hence, when every term of sin²x + cos²x = 1 is divided by sin²x, we end up with another new identity of 1 + cot²x = cosec²x