Prove the identity Sinx Cosx Secx Cscx Sin 2x 2Solu

Prove the identity. ( Sinx - Cosx ) / ( Secx - Cscx ) = Sin (2x) / 2

Solution

( Sinx - Cosx ) / ( Secx - Cscx )

write secx as 1/cosx , cscx as 1/sinx

=( sinx - cosx ) / ((1/cosx) -(1/sinx) )

=( sinx - cosx ) / ((sinx-cosx)/(cosx sinx))

=( sinx - cosx )(cosx sinx) /(sinx-cosx)

=(cosx sinx)

=(2cosx sinx) /2

=(sin2x)/2