# Math Help - trigonometric identities

1. ## trigonometric identities

Could someone please tell me if I done this correctly?

Verify the identity

$
cot^2 x - cos^2 x = cot^2 x cos^2 x
$

$
-cos^2(-x) = cos^2 x
$

So:
$
cot^2 x cos^2 x
$

2. $
cot^2 x - cos^2 x = cot^2 x \cdot cos^2 x
$

$
\frac{cos^2 x}{sin^2 x} - cos^2 x = \frac{cos^2 x}{sin^2 x} \cdot cos^2 x
$

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

$
cosec^2 x = cot^2 x +1
$

The well known identity you can easily check. Multiply by $
sin^2 x
$

$
1 - sin^2 x = cos^2 x
$

$
1 = cos^2 x + sin^2 x
$