really hard verifying trig identity.

[spillthestars]

I'm having really bad trouble with a few trig identities..if anyone could help that'd be great.

Problem 1 -

2sinx cosx
---------------- = sinx + cosx + 1
sinx + cosx -1


Problem 2 -

sinx - cosx - 1 - cosx + 1
----------------- = ------------
sinx + cosx - 1 sinx

(Note the negative sign in the second fraction can be used for the bottom or the top)


I really appreciate this if anyone can help me out

 

[Gene]

1) multiply thr RHS by
(sin(x)+cos(x)-1)/(sin(x)+cos(x)-1)

2) your note is not correct unless you mean

sin(x) - cos(x) - 1   -(cos(x) + 1) 
-------------------- = ------------ 
sin(x) + cos(x) - 1        sinx

 

[spillthestars]

I don't understand what you are saying sorry.
I don't understand the layout of what you wanted me to try.

SO i did that and got this for the right side, now I'm not sure where to go...


2sinx + 2cos -1
----------------
sinx + cosx - 1

 

[Gene]

When you do the multiplication the denominators become the same and the numerator goes
((sin(x)+cos(x))+1)* ((sin(x)+cos(x))-1)=
((sin(x)+cos(x))²-1 =
((sin²(x)+2sin(x)cos(x)+cos²(x))-1=
2sin(x)cos(x)

(The last step uses sin²+cos²=1)