Question

tan thitha -cot thitha /sin thitha ×cos thitha = tan² thitha- cot²thitha​

Answer 1

Answer:

LHS,

$\frac{ \tan( \alpha ) - \cot( \alpha ) }{ \sin( \alpha ) \cos( \alpha ) } = ( \frac{ \sin( \alpha ) }{ \cos( \alpha ) } - \frac{ \cos( \alpha ) }{ \sin( \alpha ) } ) \times \frac{1}{ \sin( \alpha ) \cos( \alpha ) }$

$= \frac{ {sin}^{2} \alpha - {cos}^{2} \alpha }{ {sin}^{2} \alpha \: {cos}^{2} \alpha } = \frac{1}{ {cos}^{2} \alpha } - \frac{1}{ {sin}^{2} \alpha } =$

${sec}^{2} \alpha - {cosec}^{2} \alpha = 1 + {tan}^{2} \alpha - 1 - {cot}^{2} \alpha = {tan}^{2} \alpha - {cot}^{2} \alpha$

RHS.

Proved.