# really hard verifying trig identity.

#### spillthestars

##### New member
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

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

2) your note is not correct unless you mean
Code:
sin(x) - cos(x) - 1   -(cos(x) + 1)
-------------------- = ------------
sin(x) + cos(x) - 1        sinx

#### spillthestars

##### New member
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

##### Senior Member
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)