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

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

2. If sinθ + cosθ = √2 (where 0° < θ < 90°), then the value of θ is

(a) 30° (b) 45° (c) 60° (d) 90°

3. If \(r\cosθ = 2\sqrt{3}\), \(r\sinθ = 2\), and \(0° < θ < 90°\), then find the values of \(r\) and \(θ\).

4. Two tangents are drawn to a circle from points P and Q, and they intersect at point A. If ∠PAQ = 80°, then what is the value of ∠APQ?

5. ABCD is a cyclic quadrilateral. If BC is the diameter and ∠ADC = 130°, then what is the value of ∠ACB?

6. In triangle △ABC, if ∠ABC = 90°, AB = 5 cm, and BC = 12 cm, then what is the radius of its circumcircle?

7. In triangle ABC, ∠B = 90°, and BC = \(\sqrt{3}\) × AB. What is the value of \(\sin C\)?

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

8. In the cyclic quadrilateral ABCD, if \(\angle\)DBA = 50° and \(\angle\)ADB = 33°, then what is the value of \(\angle\)BCD?

9. In \(\triangle\)ABC, \(\angle\)ABC = 90°, and BD \(\bot\) AC. If BD = 6 cm and AD = 4 cm, then what is the length of CD?

10. If \( r \cos θ = 2\sqrt{3} \), \( r \sin θ = 2 \), and \( 0° < θ < 90° \), then find the values of both \( r \) and \( θ \).

11. If \( \csc^2 θ = 2\cot θ \) and \( 0° < θ < 90° \), then find the value of \( θ \).

12. If triangle ABC is a right-angled triangle with ∠C = 90°, BC = 21 units, and AB = 29 units, then find the values of sin A, cos A, sin B, and cos B.

13. If \(\sec \theta = \csc \phi\), where \(0^\circ < \theta < 90^\circ\) and \(0^\circ < \phi < 90^\circ\), then the value of \(\sin(\theta + \phi)\) is 1.