Please see attached verification of the below trig identities The only part I don’t understand is the complex

Question

Please see attached verification of the below trig identities. The only part I don’t understand is the complex

conjugate part

  1. wth is a complex conjugate? those two lines below the red don’t make sense to me at all, please break it down.
  2. Why do complex conjugates allow us to muiply cosx/1+sinx by 1-sinx/1-sinx?

This is in my advanced functions course and the idea of complex conjugates was introduced with no context at all. Please explain as much as possible. Thanks!

+ since +
cosse
2 secx
cos)C
1 + since
. Use Complex Conjugates
( at bi) ( a – bi)
az + bi – bi – biz = Q2 + be
( + sin )
cosx
1 – since – 2 secx
cos XC
– 1 + sink
1 – since
1 – since+link – size
= 1 – sin 30
= cos
cosxe ( 1 – since )
cofu
+ sink ,
1 – sink – 2 secx
cost
COJVC
It sink + ( -since = 2 keck
cos 2C
V –
2
coJ 2C
Cost
Math