Question

what will be the result when each term of sin^2 theta + cos^2theta =1 is divided by sin^2theta​...

Answer 1

${sin}^{2} \: \theta + {cos}^{2} \: \theta = 1$

$each \: term \: divided \: by \: {sin}^{2} \: \theta$

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

Formula used :

$\frac{cos \: \theta}{sin \: \theta} = cot \: \theta$

$\frac{1}{sin \: \theta} = cosec \: \theta$