The image you provided is slightly blurred, but I'll do my best to extract the mathematical content and solve each part. Let's begin:

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Extracted Problem

The image contains multiple parts that seem to involve various calculations and mathematical concepts. Here’s what I can extract and solve:

1. Problem 1 involves calculating something related to a formula or expression involving trigonometric or algebraic operations.

2. Problem 2 appears to involve calculating or deriving another mathematical expression or evaluating a given condition.

Given the limitations of the image quality, I can provide an estimated interpretation and a step-by-step solution for the first few lines that I can extract.

Solution Outline

1. Problem 1: Trigonometric/Algebraic Calculation

• It seems like there is an expression involving trigonometric functions or polynomial expressions.
• The formula or expression might need simplification or evaluation.

2. Problem 2: Evaluation or Derivation

• This part seems to involve evaluating a function or derivative.
• Could be related to calculus or algebra.

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Detailed Solution (Assumed Parts)

Given that the text is not entirely clear, I'll work through a few common steps that might relate to the content based on the partial information:

1. Step 1: Simplify the Expression

   • Assume an algebraic or trigonometric expression, say $\cos^2(x) + \sin^2(x)$. Simplifying this would result in $1$, based on the Pythagorean identity.

2. Step 2: Derivative Calculation

   • If the problem involves a derivative, for example, $\frac{d}{dx}[\sin(x)]$, then the derivative is $\cos(x)$.

3. Step 3: Evaluate at a Point

   • If you're required to evaluate a function at a specific point, e.g., $f(x) = x^2$ at $x = 2$, then $f(2) = 4$.

Next Steps

Given the assumptions, if these general methods align with your expected problems, I can continue solving the exact parts once the image is clearer or you provide more specific text.

Would you like to clarify the content, or is there a specific part you want to focus on? I’m happy to assist further!

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Relative Questions

1. How do you simplify trigonometric identities like $\cos^2(x) + \sin^2(x)$?
2. What is the general method for finding the derivative of a basic function?
3. How do you evaluate a function at a given point?
4. What are some common mistakes when simplifying algebraic expressions?
5. How do you approach solving trigonometric equations involving multiple angles?

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Tip

When working with blurry or unclear images, try to focus on key symbols or numbers, as these can provide clues to the overall problem structure.