Reciprocal identity : sec x = 1/cos x
Ratio identity : tan x = sinx/cos x
= ((1/cosx)+(sinx/cosx))((1- sinx)/cosx)
= ((1+ sinx)/cosx)((1- sinx)/cosx)
= ((1- sin²x)/cos²x) (Since (a+b)(a-b) = a² - b² )
Pythagorean identity: cos²x = 1- sin²x.
=cos²x/cos²x
=1
= Right hand side identity.