(tga*cosa)2-1

To simplify the expression \((\tan(a) \cos(a))^2 - 1\), we can follow these steps:

1. Expand the squared term: \[ (\tan(a) \cos(a))^2 = \tan^2(a) \cos^2(a) \]

2. Use the identity for tangent: Recall that \(\tan(a) = \frac{\sin(a)}{\cos(a)}\). Therefore, \(\tan^2(a) = \frac{\sin^2(a)}{\cos^2(a)}\).

Substituting this, we have: \[ \tan^2(a) \cos^2(a) = \frac{\sin^2(a)}{\cos^2(a)} \cdot \cos^2(a) = \sin^2(a) \]

3. Substituting back into the expression: \[ \tan^2(a) \cos^2(a) - 1 = \sin^2(a) - 1 \]

4. Use the Pythagorean identity: Recall that \(\sin^2(a) + \cos^2(a) = 1\). Therefore, \(\sin^2(a) - 1 = -\cos^2(a)\).

So, the simplified expression is: \[ (\tan(a) \cos(a))^2 - 1 = -\cos^2(a) \]

In conclusion, \[ (\tan(a) \cos(a))^2 - 1 = -\cos^2(a). \]