The expression shown in the image is:

$\sec \theta - \tan \theta \sin \theta$

Let's simplify it step by step.

Step 1: Recall trigonometric identities.

We know that: $\sec \theta = \frac{1}{\cos \theta}$ and $\tan \theta = \frac{\sin \theta}{\cos \theta}$

Step 2: Substitute the identity for $\tan \theta$.

The given expression becomes: $\sec \theta - \left(\frac{\sin \theta}{\cos \theta}\right)\sin \theta$

Step 3: Simplify the second term.

The second term simplifies to: $\frac{\sin^2 \theta}{\cos \theta}$

Thus, the expression now becomes: $\frac{1}{\cos \theta} - \frac{\sin^2 \theta}{\cos \theta}$

Step 4: Combine the terms.

Since both terms have the same denominator, we can combine them: $\frac{1 - \sin^2 \theta}{\cos \theta}$

Step 5: Use the Pythagorean identity.

We use the Pythagorean identity: $1 - \sin^2 \theta = \cos^2 \theta$

Thus, the expression simplifies to: $\frac{\cos^2 \theta}{\cos \theta}$

Step 6: Simplify further.

Finally, simplify the fraction: $\cos \theta$

So, the simplified form of the expression is: $\boxed{\cos \theta}$

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you derive the Pythagorean identity $1 - \sin^2 \theta = \cos^2 \theta$?
2. What is the relationship between $\sec \theta$ and $\cos \theta$?
3. Can you apply similar steps to simplify the expression $\sec^2 \theta - \tan^2 \theta$?
4. How does the simplification of trigonometric expressions help in solving trigonometric equations?
5. What are other common trigonometric identities used in simplifications?

Tip: Always look for common identities like the Pythagorean identities to simplify complex trigonometric expressions.