1. The values of \(\cos 54^\circ\) and \(\sin 36^\circ\) are equal.

2. Given that \(\cos\alpha = \sin\beta\) and both \(\alpha\) and \(\beta\) are acute angles, find the value of \(\sin(\alpha + \beta)\).

3. The numerical values of the circumference and the area of a circular region are equal. The length of the diagonal of the square circumscribed about that circle is —

(a) 4 units (b) 2units (c) \(4\sqrt{2}\) units (d) \(2\sqrt{2}\) units

4. The values of \( \cos 54^\circ \) and \( \sin 36^\circ \) are equal.

5. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and curved surface area will be equal.

6. If the roots of the equation \(ax^2 + b + c = 0\) are \(\sin α\) and \(\cos α\), then what is the value of \(b^2\)?

(a) \(a^2-2ac\) (b) \(a^2+2ac\) (c) \(a^2-ac\) (d) \(a^2+ac\)

7. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

8. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

9. The values of \( \cos 54° \) and \( \sin 36° \) are equal.

10. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and its curved surface area will be equal.

11. Given that \(\sin(A + B) = 1\) and \(\cos(A - B) = 1\), where \(0^\circ \leq A + B \leq 90^\circ\) and \(A > B\), determine the values of angles \(A\) and \(B\).