You can put this solution on YOUR website! Verify the Identity?
tanx-secx/sinx=(1-cscx)secx
Start with left side:
tanx-secx/sinx
tan/sin-sec/sin
(sin/cos)/(sin)-(1/cos)/(sin)
sin/cossin-(1/cos)/(sin)
(1/cos)-(1/cos)/(sin)
factor out (1/cos)
(1/cos)(1-1/sin)
secx(1-cscx)
verified:
left side=right side