Which of the following options is incorrect ?

Options

A. `sec^(4)theta-sec^(2)theta=tan^(4)theta+tan^(2)theta`
B. `cos60^(@)cos45^(@)-sin60^(@)sin45^(@)=(1)/(sqrt(2))`
C. `(sin60^(@))/(cos^(2)45^(@))-cot30^(@)+15cos90^(@)=0`
D. `sqrt((1-sintheta)/(1+sintheta))=sectheta-tantheta`

Answer

To determine which of the given options is incorrect, we will analyze the mathematical expressions provided in the options.

### Step-by-Step Solution:

1. **Understanding the Problem:**
We need to identify which option among the given choices is incorrect. The options involve trigonometric identities and values.

2. **Analyzing Option 1:**
Let's consider the expression given in option 1:
\[ \tan^4 \theta - \sec^2 \theta \]
We can use the identity \(\sec^2 \theta = 1 + \tan^2 \theta\) to rewrite the expression:
\[ \tan^4 \theta - (1 + \tan^2 \theta) = \tan^4 \theta - 1 - \tan^2 \theta \]
Now, we can factor this expression:
\[ = (\tan^2 \theta - 1)(\tan^2 \theta + 1) \]
Since \(\tan^2 \theta - 1\) can be expressed as \((\tan^2 \theta - 1)(\tan^2 \theta + 1)\), this part is correct.

3. **Analyzing Option 2:**
Now, let's check option 2:
\[ -\sin 60^\circ \cdot \sin 45^\circ \]
We know the values:
\[ \sin 60^\circ = \frac{\sqrt{3}}{2}, \quad \sin 45^\circ = \frac{1}{\sqrt{2}} \]
Substituting these values in:
\[ -\left(\frac{\sqrt{3}}{2}\right) \cdot \left(\frac{1}{\sqrt{2}}\right) = -\frac{\sqrt{3}}{2\sqrt{2}} = -\frac{\sqrt{6}}{4} \]
This calculation is correct.

4. **Conclusion:**
Since the analysis shows that the calculations for both options are correct, we need to identify which option is stated to be incorrect. The video transcript indicates that option 2 is incorrect due to a miscalculation in the sine values.

### Final Answer:
The incorrect option is **Option 2**.