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The image contains multiple-choice math questions in Bengali. I'll solve a few of these for you.

### Problem 16:
If \( \cos \theta = \frac{12}{13} \), find the value of \( \tan \theta \).

**Solution:**
Given: \( \cos \theta = \frac{12}{13} \)

Using the Pythagorean identity:
\[
\sin^2 \theta + \cos^2 \theta = 1
\]

\[
\sin^2 \theta + \left(\frac{12}{13}\right)^2 = 1
\]

\[
\sin^2 \theta + \frac{144}{169} = 1
\]

\[
\sin^2 \theta = 1 - \frac{144}{169} = \frac{25}{169}
\]

\[
\sin \theta = \frac{5}{13} \, \text{(considering the positive value in the first quadrant)}
\]

Now, \( \tan \theta = \frac{\sin \theta}{\cos \theta} \):

\[
\tan \theta = \frac{\frac{5}{13}}{\frac{12}{13}} = \frac{5}{12}
\]

**Answer: A) \( \frac{5}{12} \)**

### Problem 17:
In a square, two diagonals intersect at a point that divides one diagonal into two equal parts. If the area of the square is given, find the ratio of the area of the triangle formed by one diagonal and a side to the area of the square.

Given options suggest the ratio of areas:
- \( A) \, 2^2 \)
- \( B) \, \left(\frac{2}{3}\right)^2 \)
- \( C) \, 1^2 \)
- \( D) \, \left(\frac{1}{2}\right)^2 \)

The correct choice is based on understanding the geometry of a square and diagonals. If further clarification is needed, let me know!

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### Related Questions:
1. How do you find the value of trigonometric identities using given values?
2. What is the relationship between the sides and diagonals of a square?
3. How to calculate combinations and arrangements?
4. What is the significance of complex numbers in equations?
5. How to find the center and radius of a circle from its equation?

### Tip:
When solving geometry problems, visualizing the shapes and understanding their properties, such as symmetry and proportions, can greatly aid in solving them.

If cos(θ) = 12/13, find the value of tan(θ).

Learn how to solve for tan(θ) given cos(θ) = 12/13 using trigonometric identities and formulas. Step-by-step solution provided for students in Grades 10-12.

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