+0  
 
0
663
1
avatar+466 

Show that: (tan x - sec x)2 = (1 - sin x)/(1 + sin x)

 Mar 17, 2016
 #1
avatar+129852 
+5

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

 

tan^2x - 2tanxsecx + sec^2x     

 

tan^2x - 2tanxsecx + [ tan^2x + 1 ]

 

2tan^2x -2tanxsecx + 1

 

2sin^2x/cos^2x  - 2 [sinx]/cos^2x  + [cos^2x / cos^2x ]

 

[ 2sin^2x - 2sinx  + cos^2x] /  cos^2x

 

[ 2sin^2x - 2sinx + (1 - sin^2x ) ] / cos^2x

 

[sin^2x - 2 sinx + 1] / cos^2x          factor the numerator

 

[sinx -1] [sinx - 1]  / [ 1 - sin^2x] 

 

[sinx -1]  [sinx - 1 ] / (  [ 1 + sinx ] [ 1 - sinx] )        factor  -1  out of the numerator

 

- [ 1 - sinx] [ sinx - 1] / ([1 + sinx] [ 1 - sinx ] )

 

- [sinx -1]  / [ 1 + sinx]

 

[1 - sin x ] / [ 1 + sin x ]

 

 

 

 

cool cool cool

 Mar 17, 2016

0 Online Users