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

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

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

4. 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.

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

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

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

8. If \(sinθ−cosθ=0,\) \( (0°<θ<90°)\) and \(secθ+cosecθ=x\), then the value of \(x\) is—?

(a) \(1\) (b) \(2\) (c) \(\sqrt2\) (d) \(2\sqrt2\)

9. If \(x\sin45^\circ \cos45^\circ \tan60^\circ = \tan^2 45^\circ - \cos^2 60^\circ\), then what is the value of \(x\)?

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

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

11. 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 \(x\).

12. 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 \(x\).

13. If one root of the quadratic equation \(x^2 + ax + 12 = 0\) is 1, then the value of \(a\) will be —.

14. If \(x^2 - \frac{5}{6}x + \frac{1}{6} = 0\), then the value of \(x\) is -

(a) \(\cfrac{1}{2}, \cfrac{1}{3}\) (b) 2, 3 (c) 3, 4 (d) 3, 4

15. If the product of the roots of the equation \(x^2 - 2x + k = 8\) is \(-2\), then the value of \(k\) is—

(a) -2 (b) 6 (c) 1 (d) -6

16. If the product of the roots of the equation \(x^2 - 3x + k = 10\) is \(-2\), then the value of \(k\) is —

(a) -2 (b) -8 (c) 8 (d) 12

17. 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 \(y\).