tan x1 sec x 1 sec xtanx 2 csc x Solutiontanx1 secx 1 s

tan x/1 + sec x + 1 + sec x/tanx - 2 csc x

tanx/(1 +secx) + (1 +secx)/tanx -2cscx

first solve the terms : tanx/(1 +secx) + (1 +secx)/tanx

taking lcd as (1 +secx)tanx:

[ tan^2x + (1+secx)^2 ]/tanxsecx

= ( tan^2x +1 +sec^2x + 2secx) /tanxsecx

use the identity : 1 +tan^2x = sec^2x

=( 2sec^2x +2secx)/tanxsecx

= 2secx(secx +1)/tanxsecx

= 2(1+ secx)/tanx

Now, tanx/(1 +secx) + (1 +secx)/tanx -2cscx = (2 +2secx)/tanx - 2cscx

= [2 +2secx -2 secx]/tanx

=2/tanx

= 2cotx