Proving Identities Trig part 2

[Louise Johnson]

Need some help
Prove the identities:

#1 sin(x+y)-sin(x-y)=2cosxsiny
Answer: ( I think i got through this one)
sinxcosy+cosxsiny-(sinxcosy-cosxsiny)
sinxcosy+cosxsiny-sinxcosy+cosxsiny
sinxcosy-sinxcosy+cosxsiny+cosxsiny
cosxsiny+cosxsiny
2(cosxsiny)

#2
1/1+sinx=sec^2x-tanx/cosx

This one I am having big problems with including what identities to use....Arggggg!!
Any help would be great!

 

[arthur ohlsten]

sin[x+y]-sin[x-y]=?2cosxsiny
sinxcosy+cosxsiny -[sinxcosy-cosxsiny]=?2cosxsiny
2cosxsiny=?2cosxsiny yes
==============================
1/[1+sinx]=?sec^2x-tanx/cosx
1/[1+sinx]=? 1/cos^2x - sinx/cos^2x
1/[1+sinx]=? [1-sinx]/cos^2x yes

Arthur

 

[Louise Johnson]

yippeeee finally got one correct. That second one I have been staring at for some time and now looking at your answer probably for an even longer time.
Hope I get it together soon.
Thank you
Louise

 

[Louise Johnson]

I think I solved/completed it with your help

1/[1+sinx]=? [1-sinx]/cos^2x

use the identity of 1-sin^2x for cos^2x

Then 1-sinx/1-sin^2x = 1-sinx/(1+sinx)(1-sinx)

LHS =1/1+sinx