Question

cosec theta -cot theta whole square =1- cos theta / 1 +cos theta

pls tell

Answer 1

Answer:

Step-by-step explanation :

Answer 2

${\large{\maltese}} \: \: \: \: \: { \underline{ \underline{\bf{\Large{Solution : }}}}}$

$\dashrightarrow \: \: \: \sf \frac{1 - \cos \theta}{1 + \cos \theta}$

$\dashrightarrow \: \: \: \sf \frac{(1 - \cos \theta)(1 - \cos \theta)}{(1 + \cos \theta)(1 - \cos \theta)}$

$\dashrightarrow \: \: \: \sf \frac{{ \big(1 - \cos \theta \big)}^{2} }{ \big(1 - { \cos}^{2} \theta \big) }$

$\dashrightarrow \: \: \: \sf \frac{1 + { \cos}^{2} \theta - 2 \cos \theta }{ { \sin}^{2} \theta }$

$\dashrightarrow \: \: \: \sf \frac{1}{ { \sin}^{2} \theta} + \frac{ { \cos}^{2} \theta }{ { \sin}^{2} \theta} - \frac{2 \cos \theta}{ { \sin}^{2} \theta }$

$\dashrightarrow \: \: \: \sf { \cosec}^{2} \theta + { \cot}^{2} \theta - 2 \cot \theta \cosec \theta$

$\dashrightarrow \: \: \: {\bf { \bigg( \cosec \theta - \cot \theta \bigg)}^{2} }\: \: \: \: \: \: \: \: \: \:{ \color{skyblue}{Hence\:\:Proved}}$