Question

prove that

tan A - cot A= ( 2sin^2A-1)/(sinA×cos A)​

Answer 1

Answer:

CotA- tanA

=cosA/sinA- sinA/cosA

=cos^2A-sin^2A)/sinAcosA

=cos^2A-(1-cos^2A)/sinAcosA

=cos^2A-1+cos^2A/sinAcosA

=2cos^2A-1/sinAcosA

Step-by-step explanation:

Answer 2

Answer:

$\tan( \alpha ) - \cot( \alpha ) = \frac{2 { \sin( \alpha ) }^{2} - 1}{ \sin( \alpha ) \cos( \beta )} \\ \tan( \alpha ) - \cot( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } - \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ = \frac{ { \sin( \alpha ) }^{2} - { \cos( \alpha ) }^{2} }{ \sin( \alpha ) \cos( \alpha ) } \\ \frac{ { \sin( \alpha ) }^{2} - (1 - { \sin( \alpha ) }^{2} }{ \sin( \alpha ) \cos( \alpha ) } \\ = \frac{2 { \sin( \alpha ) - 1 }^{2} }{ \sin( \alpha ) \cos( \alpha ) }$