1. Find the value of: \( \sec^2 45^\circ - \cot^2 45^\circ - \sin^2 30^\circ - \sin^2 60^\circ \)

2. Find the value of: \( 3 \tan^2 45^\circ - \sin^2 60^\circ - \cfrac{1}{3} \cot^2 30^\circ - \cfrac{1}{8} \sec^2 45^\circ \)

3. Find the value of: \( \cot^2 30^\circ - 2 \cos^2 60^\circ - \cfrac{3}{4} \sec^2 45^\circ - 4 \sin^2 30^\circ \)

4. If \(x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ\), then the value of \(x\) is —

(a) \(\pm 1\) (b) \(\pm \cfrac{1}{2}\) (c) \(\pm \cfrac{1}{\sqrt2}\) (d) \(\pm \cfrac{1}{\sqrt3}\)

5. If \(x = \sin^2 30^\circ + 4 \cot^2 45^\circ - \sec^2 60^\circ\), find the value of \(x\).

6. If \(x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ\), then what is the value of \(x\)?

7. If \(x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ\), find the value of \(x\). Let me know if you'd like a step-by-step solution next. I'm ready when you are.

8. If \(x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ\), find the value of \(x\).

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

10. If \(x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ\), then find the value of \(x\).

11. If \(x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ\), then find the value of \(x\).

12. Evaluate the expression: \(\cot^2 30^\circ - 2\cos^2 60^\circ - \cfrac{3}{4}\sec^2 45^\circ - \sin^2 30^\circ\)

13. Find the value of: \( \cfrac{4}{3} \cot^2 30^\circ + 3 \sin^2 60^\circ - 2 \csc^2 60^\circ - \cfrac{3}{4} \tan^2 30^\circ \)

14. Evaluate the expression: \[ \cot^2 30^\circ - 2\cos^2 60^\circ - 4\sin^2 30^\circ - \frac{3}{4}\sec^2 45^\circ + \tan 45^\circ \]

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

16. Find the value of: \[ \frac{2\tan^2 30^\circ}{1 - \tan^2 30^\circ} + \sec^2 45^\circ - \cot^2 45^\circ - \sec 60^\circ \]

17. Find the value of: \( \cfrac{\cfrac{1}{3} \cos 30^\circ}{\cfrac{1}{2} \sin 45^\circ} + \cfrac{\tan 60^\circ}{\cos 30^\circ} \)

18. Find the value of: \( \sec^2 60^\circ - \cot^2 30^\circ - \cfrac{2 \tan 30^\circ \csc 60^\circ}{1 + \tan^2 30^\circ} \)

19. Evaluate: \[ 3\tan^2 45^\circ - \sin^2 60^\circ - \frac{1}{3} \cot^2 30^\circ - \frac{1}{8} \sec^2 45^\circ \]

20. If \(x \sin 60^\circ \cos^2 30^\circ = \frac{\tan^2 45^\circ \sec 60^\circ}{\csc 60^\circ}\), find the value of \(x\).

21. Solve: \[ x^2 = \sin^2 30^\circ + 4\cot^2 45^\circ - \sec^2 60^\circ \]

22. Evaluate the expression: \[ \frac{1 - \sin^2 30^\circ}{1 + \sin^2 45^\circ} \times \frac{\cos^2 60^\circ + \cos^2 30^\circ}{\csc^2 90^\circ - \cot^2 90^\circ} \div (\sin 60^\circ \tan 30^\circ) \]

23. If \((x + 1)\cot^2\frac{\pi}{2} = 2\cos^2\frac{\pi}{3} + \frac{3}{4}\sec^2\frac{\pi}{4} + 4\sin^2\frac{\pi}{6}\), then find the value of \(x\).

24. If \[ x \cos 60^\circ = \frac{2 \tan 45^\circ}{1 + \tan^2 45^\circ} - \frac{1 - \tan^2 30^\circ}{1 + \tan^2 30^\circ} \] then find the value of \(x\).

25. Find the value of \(\cfrac{4}{\sec^2\theta}+\cfrac{1}{1+\cot^2\theta}+3\sin^2\theta\).

26. The English translation is: "If \(x^2 = \sin^2 30° + 4\cot^2 45° - \sec^2 60°\), determine the value of \(x\)."

27. If \(x \tan 30^\circ + y \cot 60^\circ = 0\) and \(2x - y \tan 45^\circ = 1\), then calculate and write the values of \(x\) and \(y\).

28. The value of \(\frac{1}{\sec^2\theta} + \frac{1}{1 + \cot^2\theta} + 3\sin^2\theta\) is _____

29. If \( \frac{1}{\sec^2\theta} + \frac{1}{1 + \cot^2\theta} + 3\sin^2\theta \), then its value is _____.

30. What is the value of \(\frac{4}{\sec^2\theta} + \frac{1}{1 + \cot^2\theta} + 3\sin^2\theta\)?