Question

3x = sec theta, 3/x = tan theta
Find (x^2 -1/x^2)

Answer 1

$3x = \frac{1}{ \cos( \alpha ) } \\ \frac{3}{x} = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ \cos( \alpha ) = \frac{1}{3x} \\ \frac{3}{x} = \frac{ \sin( \alpha ) }{ \frac{1}{3x} } \\ \frac{3}{x} = 3x \sin( \alpha ) \\ \frac{1}{ {x}^{2} } = \sin( \alpha ) \\ find \ \: {x}^{2} - \frac{1}{ {x}^{2} } \\ \csc( \alpha ) - \sin( \alpha ) \\ \frac{1}{ \sin( \alpha ) } - \sin( \alpha ) \\ \frac{1 - { \sin( \alpha ) }^{2} }{ \sin( \alpha ) } \\ \frac{ { \cos( \alpha ) }^{2} }{ \sin( \alpha ) } \\ \cot( \alpha ) \cos( \alpha )$