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It looks like you've uploaded a section of a trigonometric expression. I can help with the math problem visible in the image. Let's focus on part **d)**:

\[
\cos\left(\frac{3\pi}{2} - a\right) - \sin\left(\frac{3\pi}{2} - a\right) + \cos\left(a - \frac{\pi}{2}\right) - \sin\left(a - \frac{\pi}{2}\right)
\]

We can simplify this expression by using trigonometric identities:

1. **Cosine of a difference**: 
   \[
   \cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)
   \]
2. **Sine of a difference**: 
   \[
   \sin(x - y) = \sin(x)\cos(y) - \cos(x)\sin(y)
   \]

For specific angles like \( \frac{3\pi}{2} \) and \( \frac{\pi}{2} \), we can use standard values of trigonometric functions:

- \(\cos\left(\frac{3\pi}{2}\right) = 0\), \(\sin\left(\frac{3\pi}{2}\right) = -1\)
- \(\cos\left(\frac{\pi}{2}\right) = 0\), \(\sin\left(\frac{\pi}{2}\right) = 1\)

I'll now proceed with the simplifications.The given expression simplifies to:

\[
2 \cos(a)
\]

Would you like further details on the simplification process or have any additional questions?

Here are 5 related questions you could explore:

1. What are the key trigonometric identities used in simplifying expressions?
2. How do the values of sine and cosine change at specific angles like \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\)?
3. Can you simplify an expression with different trigonometric identities, such as double angle or sum-to-product formulas?
4. How do transformations like \(\sin(x - y)\) and \(\cos(x - y)\) work in general cases?
5. How does this simplification apply to solving trigonometric equations?

**Tip:** When simplifying trigonometric expressions, always remember to check if the angles involved correspond to known standard values (like \( \frac{\pi}{2}, \pi, \frac{3\pi}{2} \)) to streamline the process.

Simplify the trigonometric expression involving cosine and sine: cos(3π/2 - a) - sin(3π/2 - a) + cos(a - π/2) - sin(a - π/2)

Simplify a trigonometric expression involving cos(3π/2 - a) - sin(3π/2 - a) and cos(a - π/2) - sin(a - π/2). The problem uses trigonometric identities to simplify the terms, resulting in a concise expression.

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