Dengan menggunakan identitas trigonometri, sederhanakan setiap bentuk berikut ini : a) (tan x + sec x) (tan x – sec x) b) 1 / (1 + cos x) + 1 / (1 – cos x) c) tan x – sec² x / tan x d) (cos x) / (1+ sin x) + (1+sin x) / (cos x)

A. (tan x +sec x) (tan x -sec x)
=tan²x -sec² x
=tan²x – (1 +tan²x)
=tan²x -1 -tan²x
=-1
B. 1/(1 +cos x) + 1/(1 -cos x)
= 1 -cos x +1 +cos x/1 -cos²x
=2/sin²x
=2csc²x
C. tan x -(sec²x/tan x)
=(tan²x -sec²x)/tan x
=( tan²x -(1 +tan²x))/tan x
=(tan²x -1 -tan²x)/tan x
=-1/tan x
=-cos x/sin x
=-cot x
D. cos x/(1 +sin x) +1 +sin x/(cos x)
=cos²x +1 +2sin x +sin²x/(1 +sin x)
(cos x)
=1 -sin²x +1 +2sin x +sin²x/(1 +sin x)
(cos x)
= 2 +2sin x/(1 +sin x) (cos x)
= 2 (1 +sin x) /(1 +sin x) (cos x)
=2/cos x
= 2sec x