1. ( tan x – sec x) (sin x + 1)=….

A) (tan x – sec x)(sin x +1)
= (tan x – sec x)(tan x + sec x)(sin x + 1)(sin x – 1)
= (tan^2 x – sec^2 x)(sin^2 x – 1)
= (tan^2 x –(1 + tan^2 x)(1 – cos^2 x – 1)
= (tan ^2 x -1 – tan^2 x)(- cos^2 x)
= (-1)( – cos^2 x)
= cos^2 x

b) sec^2 x / 1 + cot^2 x
= sec^2 x / cosec^2 x
=    1       :     1    
   cos^2 x    sin^2 x
=    1       x  sin^2 x
   cos^2 x        1
= sin^2 x / cos^x
= tan^2 x

c) cos^x / 1 – sin x
=   cos x    x  (1 + sin x)   
  (1 – sin x)     (1 + sin x)
= cos x(1 + sin x) / 1 – sin^2 x
= cos x(1 + sin x) / cos^2 x
= 1+ sin x / cos x

semoga bisa membantu. mohon diberitahu jika ada kesalahan.. 🙂