1. ## Trigonometric simplification

I worked a derivative problem all the way down to this:

$\frac {-csc^2 x}{(cot + 1)^2}$

Answer: $\frac {-1}{(sinx + cosx)^2}$

I'm pretty sure there is a way to simplify this, but I don't see how, even after studying trigonometric identities.

I think $csc^2 + cot^2= 1$ has something to do with this.

Or maybe make csc and cot as their corresponding sin and cos values...

I'm just not sure!!!

By

2. Originally Posted by Truthbetold
I worked a derivative problem all the way down to this:

$\frac {-csc^2 x}{(cot + 1)^2}$

Answer: $\frac {-1}{(sinx + cosx)^2}$

I'm pretty sure there is a way to simplify this, but I don't see how, even after studying trigonometric identities.

I think $csc^2 + cot^2= 1$ has something to do with this.

Or maybe make csc and cot as their corresponding sin and cos values...

I'm just not sure!!!

By
$-\frac{csc^2(x)}{cot(x) + 1}$

$= -\frac{\frac{1}{sin^2(x)}}{\frac{cos(x)}{sin(x)} + 1}$

$= -\frac{1}{sin(x) cos(x) + sin^2(x)}$

$= -\frac{1}{sin(x) ~ (cos(x) + sin(x) )}$

There is no way this is going to turn into
$-\frac{1}{(sin(x) + cos(x))^2} = -\frac{1}{1 + 2sin(x)cos(x)}$

-Dan