Question

TanX/Senx + cscxcotx= secxcsc2 x

Answer 1

$\frac{ \frac{ \sin(?) }{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{1} } + \frac{1}{ \sin( \alpha ) } \times \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = \frac{1}{ \cos( \alpha ) } \times \frac{1}{ {sin}^{2} ( \alpha )} \\ \frac{1}{ \cos( \alpha ) } + \frac{ \cos( \alpha ) }{ {sin}^{2} ( \alpha )} = \frac{1}{ \cos( \alpha ) {sin}^{2}( \alpha ) } \\ \frac{ {sin}^{2} ( \alpha ) + {cos}^{2} ( \alpha )}{ \cos( \alpha ) {sin}^{2}( \alpha ) } = \frac{1}{ \cos( \alpha ) {sin}^{2} ( \alpha )} \\ \frac{1}{ \cos( \alpha ) {sin}^{2}( \alpha ) } = \frac{1}{ \cos( \alpha ) {sin}^{2}( \alpha ) }$
Al final aplicamos la identidad:
${sin}^{2} ( \alpha ) + {cos}^{2} ( \alpha ) = 1$