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The problem presented in the image asks to find the value of angle \( A \) based on the following equation:

\[
\cot A = \frac{1}{\tan A} = \frac{\sqrt{3}}{1}
\]

This simplifies to:

\[
\cot A = \sqrt{3}
\]

From trigonometric identities, we know that \( \cot A = \frac{1}{\tan A} \), and from common angle values, \( \cot 30^\circ = \sqrt{3} \).

Therefore, the value of angle \( A \) is:

\[
A = 30^\circ
\]

Would you like more details on how this conclusion was reached?

Here are 5 related questions for further exploration:
1. How does \( \cot A \) relate to \( \tan A \)?
2. What are the exact trigonometric values for \( 45^\circ \) and \( 60^\circ \)?
3. How can we derive \( \cot \theta \) from the unit circle?
4. What is the significance of complementary angles in trigonometry?
5. How can we apply cotangent in real-world applications, like angles of elevation?

**Tip:** Memorizing standard trigonometric values for common angles like \( 30^\circ \), \( 45^\circ \), and \( 60^\circ \) helps speed up calculations in many problems.

Find the value of angle A given the equation: cot A = sqrt(3).

Learn how to find the value of angle A where cot(A) = sqrt(3). This problem introduces key trigonometric identities and their applications, focusing on the cotangent function and its relationship with the tangent function. Suitable for students in Grades 9-11.

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