Identities

Also this one: (cot x -1)/(1 - tan x) = csc x/sec x

tan^2(x) / [ sec(x) + 1]  =   sec(x) - 1

[sec^2(x) - 1] / [ sec(x) + 1 ]       =    sec(x) - 1

[(sec(x) + 1) (sec(x) - 1)] /  [sec(x) + 1]  =       sec(x) - 1

sec(x) - 1      =   sec(x) - 1

[cotx -1] / [1 - tanx]    =  cscx / secx

[(cotx -1) (1 + tanx)] /  [ (1- tanx) (1 + tanx)]      =    (1/sinx) / (1 / cosx)

[cotx - 1 +cotx*tanx - tanx] / [ (1- tanx) (1 + tanx)]   =  (1/sinx)* (cosx)/1

[cotx - 1 + 1 - tanx] / [ (1 - tanx)(1 + tanx)]   =      cosx / sinx

[ cotx - tanx] / [ 1 - tan^2 x]       =     cot x

[ cosx/sinx - sinx/cosx]  /  [ 1 - tan^2x]     = cot x

[( cos^2x - sin^2x) / sinxcosx] / [ 1 - sin^2x/cos^2x]    = cot x

[( cos^2x - sin^2x) / sinxcosx] / [  (cos^2x - sin^2x) / cos^2x]   = cot x

[ 1 / sinxcosx] /  [ 1 / cos^2x]    = cot x

[  1 / sinxcosx[ * [ cos^2x]   = cotx

cos^2x / [ sinxcosx]    = cot x

cosx / sinx    = cot x

cot x      = cot x