# Thread: Simplifying using trig identities

1. ## Simplifying using trig identities

Simplify: $\cot(-x) (\cos x) (\tan^2 x + 1)$

I'll show you what I have so far. My problem is I don't really know when I'm finished.

$\cot(-x) (\cos x) (\tan^2 x + 1)$
$(\frac{1}{-\tan x)})(\frac{1}{\sec x})(\sec^2 x)$
$(\frac{1}{-\tan x})(\sec x)$

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

and I have my final answer as $\frac{-\sin x}{\cos^2 x}$

Is this where I should end it, or should I keep going?

Thanks.

2. Originally Posted by Savior_Self
Simplify: $\cot(-x) (\cos x) (\tan^2 x + 1)$

I'll show you what I have so far. My problem is I don't really know when I'm finished.

$\cot(-x) (\cos x) (\tan^2 x + 1)$
$(\frac{1}{-\tan x)})(\frac{1}{\sec x})(\sec^2 x)$
$(\frac{1}{-\tan x})(\sec x)$

$(\frac{-\sin x}{\cos x})(\frac{1}{\cos x})$ NO!!!

and I have my final answer as $\frac{-\sin x}{\cos^2 x}$

Is this where I should end it, or should I keep going?

Thanks.

$(\frac{1}{-\tan x})(\sec x)$

$= \frac{-1}{\frac{\sin{x}}{\cos{x}}} \sec{x}$

$= \frac{-\cos{x}}{\sin{x}} \frac{1}{\cos{x}}$

$=\frac{-1}{sin{x}}$

$=-\csc{x}$

3. Ahhhhhh, I'm an idiot. Thanks, harish.