Find the value of `6tan^(2)theta-6sec^(2)theta`

Answer

To solve the problem \( 6\tan^2\theta - 6\sec^2\theta \), we can follow these steps:

### Step 1: Recall the Pythagorean Identity
We know from trigonometric identities that:
\[ \sec^2\theta = 1 + \tan^2\theta \]

### Step 2: Substitute the Identity
We can substitute \( \sec^2\theta \) in the expression:
\[ 6\tan^2\theta - 6\sec^2\theta = 6\tan^2\theta - 6(1 + \tan^2\theta) \]

### Step 3: Simplify the Expression
Now, distribute the \( -6 \):
\[ 6\tan^2\theta - 6 - 6\tan^2\theta \]

### Step 4: Combine Like Terms
Notice that \( 6\tan^2\theta - 6\tan^2\theta \) cancels out:
\[ -6 \]

### Final Answer
Thus, the value of \( 6\tan^2\theta - 6\sec^2\theta \) is:
\[ \boxed{-6} \]