I hope this helps you
✔sin^2x+cos^2x=1
✔ 1-tgx=1-sinx/cosx=cosx-sinx/cosx
✔1-ctgx=1-cosx/sinx=sinx-cosx/sinx
secx=1/cosx
cosecx=1/sinx
(cosx-sinx)(sinx-cosx)/sinx.cosx
cosx.sinx-cos^2x-sin^2x+sinx.cosx/sinx.cosx
2.cosx.sinx-1/sinx.cosx
2.cosx.sinx/sinx.cosx-1/sinx.cosx
2-1/sinx.cosx
2-secx.cosecx
