1. What is the value of \[ \sin 12^\circ \times \cos 18^\circ \times \sec 78^\circ \times \csc 72^\circ \]

2. What is the value of \(\cfrac{\sin \theta}{\csc \theta} + \cfrac{\cos \theta}{\sec \theta} - 2\)?

(a) 0 (b) -1 (c) 4 (d) None of the above

3. Find the value of \(x\) from the equation: \(x \sec^2 45^\circ \cdot \csc^2 45^\circ + 2(\sin 60^\circ + \sin 30^\circ) = \tan 60^\circ\)

4. Find the value of: \[ \cos^2 12^\circ + \cos^2 78^\circ + \tan^2 78^\circ - \sec^2 12^\circ \cdot \tan^2 78^\circ \]

(a) 0 (b) 1 (c) 2 (d) 3

5. Find the value of: \( \cfrac{1 - \sin^2 30^\circ}{1 + \sin^2 45^\circ} \times \cfrac{\cos^2 60^\circ + \cos^2 30^\circ}{\csc^2 90^\circ - \cot^2 90^\circ} \div (\sin 60^\circ \cdot \tan 30^\circ) \)

6. What is the value of \( \tan 4^\circ \cdot \tan 43^\circ \cdot \tan 47^\circ \cdot \tan 86^\circ \)?

(a) -1 (b) 1 (c) 0 (d) -2

7. What is the value of \( \sec^2 12^\circ - \frac{1}{\tan^2 78^\circ} \)?

(a) 0 (b) 1 (c) -1 (d) 2

8. What is the value of \( \tan 35^\circ \cdot \tan 40^\circ \cdot \tan 45^\circ \cdot \tan 50^\circ \cdot \tan 55^\circ \)?

(a) \(\cfrac{1}{\sqrt3}\) (b) \(\sqrt3\) (c) 1 (d) 0

9. Left-hand side (LHS): \[ 1 + \cfrac{\tan A}{\tan B} = 1 + \cfrac{\tan(90^\circ - B)}{\tan B} = 1 + \cfrac{\cot B}{\cot B} = 1 + \cot^2 B = \csc^2 B \] Right-hand side (RHS): \[ \tan^2 A \cdot \sec^2 B = \tan^2(90^\circ - B) \cdot \sec^2 B = \cot^2 B \cdot \sec^2 B = \cfrac{\cos^2 B}{\sin^2 B} \cdot \cfrac{1}{\cos^2 B} = \cfrac{1}{\sin^2 B} = \csc^2 B \] \(\therefore\) LHS = RHS (Proved)

10. If \[ \tan \theta \cdot \cos 60^\circ = \frac{\sqrt{3}}{2} \] then find the value of \[ \sin(\theta - 15^\circ) \] given that \(0^\circ < \theta < 90^\circ\).

11. The simplest value of \((\sin 12^\circ - \cos 78^\circ)\) is \(1\).

12. Find the value of \(x\):
\(x \sin 45° \cdot \cos 45° \cdot \tan 60° = \tan^2 45° - \cos^2 60°\)

(a) \(\cfrac{\sqrt3}{2}\) (b) \(\cfrac{1}{2}\) (c) \(\cfrac{1}{\sqrt3}\) (d) \(\sqrt3\)

13. The simplest value of \((\sin 12^\circ - \cos 78^\circ)\) is 1.

14. Evaluate the value of: \(\cfrac{\tan60^\circ - \tan30^\circ}{1 + \tan60^\circ \cdot \tan30^\circ} + \cos60^\circ \cdot \cos30^\circ + \sin60^\circ \cdot \sin30^\circ\)"