trigonometric identities

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November 26th 2008, 02:00 PM
robasc

trigonometric identities

Could someone please tell me if I done this correctly?

Verify the identity
$<br /> cot^2 x - cos^2 x = cot^2 x cos^2 x<br />$

$<br /> -cos^2(-x) = cos^2 x <br />$
So:
$<br /> cot^2 x cos^2 x<br />$
November 26th 2008, 03:03 PM
vincisonfire

$<br /> cot^2 x - cos^2 x = cot^2 x \cdot cos^2 x<br />$
$<br /> \frac{cos^2 x}{sin^2 x} - cos^2 x = \frac{cos^2 x}{sin^2 x} \cdot cos^2 x<br />$
$<br /> \frac{1}{sin^2 x} - 1 = \frac{cos^2 x}{sin^2 x}<br />$
$<br /> cosec^2 x = cot^2 x +1 <br />$
The well known identity you can easily check. Multiply by $<br /> sin^2 x<br />$
$<br /> 1 - sin^2 x = cos^2 x <br />$
$<br /> 1 = cos^2 x + sin^2 x <br />$

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