Question

(cosec theta -sin theta) ( sec theta -cos theta) sec^2 theta =tan theta​

Answer 1

$\huge\underline\bold\red{★Answer★}$

$(cosec \theta - sin \theta)(sec \theta - cos \theta) {sec}^{2} \theta \\ = ( \frac{1 - {sin}^{2} \theta}{sin \theta} )( \frac{1 - {cos}^{2} \theta }{cos \theta} ) \frac{1}{ {cos}^{2} \theta} \\ = \frac{ {sin}^{2} \theta {cos}^{2} \theta }{sin \theta cos \theta} \frac{1}{ {cos}^{2} \theta } \\ = \frac{sin \theta \: cos \theta }{cos^{2} \theta } \\ = \frac{sin \theta}{cos \theta} \\ = tan \theta$

Answer 2

Formula used :

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

$sec \: \theta = \frac{1}{cos \: \theta}$

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

Refer the attachment for complete answer