Question

Prove that cosec theta - sin theta = cot theta × cosec theta.
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Answer 1

$Step-by-step explanation:</p><p></p><p>\begin{gathered} \csc( \alpha ) - \sin( \alpha ) \\ \\ \\ = \frac{1}{ \sin( \alpha ) } - \sin( \alpha ) \\ \\ \\ = \frac{1 - { \sin}^{2} \alpha }{ \sin( \alpha ) } \\ \\ \\ = \frac{ { \cos }^{2} \alpha }{ \sin( \alpha ) } \\ \\ \\ = \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \cos( \alpha ) \\ \\ \\ = \cot( \alpha ) \cos(?) \end{gathered}csc(α)−sin(α)=sin(α)1−sin(α)=sin(α)1−sin2α=sin(α)cos2α=sin(α)cos(α)cos(α)=cot(α)cos(?)</p><p></p><p>THANKS</p><p></p><p>$