Question

Im having serious issues with verifying Trig. identities. Please help! Here is an example:

(tanX-secX)^2= 1-sinX/1+sinX

Answer 1

(sec x - tanx)^2 = (1-sinx)/(1+sinx)

use these substitutions
sin²(x) + cos²(x) = 1
cos²(x) = 1 - sin²(x)


(sec(x) - tan(x))²
=(1/cos(x) - sin(x)/cos(x))²
= (1-sin(x))² / cos²(x)
= (1-sin(x))² / (1 - sin²(x))
= (1-sin(x))² / [(1+sin(x))(1-sin(x))]
= (1-sin(x)) / (1+sin(x))