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Trigonometry Multiple Choice Questions

1. If \(\sin \theta = \frac{8}{17}\), find the value of \(\cos \theta\) and \(\tan \theta\). (a) \(\frac{15}{17}, \frac{8}{15}\) (b) \(\frac{13}{17}, \frac{7}{15}\) (c) \(\frac{11}{17}, \frac{7}{15}\) (d) None of the above

2. Find the value of \((3 \cos^2 60° + 2 \cot^2 30° – 5 \sin^2 45°)\). (a) \(\frac{11}{4}\) (b) \(\frac{13}{4}\) (c) \(\frac{15}{4}\) (d) \(\frac{17}{4}\)

3. The simplified value of \(\frac{\sin\theta}{1 + \cos \theta} + \frac{1 + \cos \theta}{\sin\theta}\) is (a) \(-2 \csc \theta\) (b) \(2 \csc \theta\) (c) \(2 \sec \theta\) (d) None of these

4. \(\triangle ABC\) is right angled at \(A\). Find the value of \(\cot B\). (a) \(\frac{5}{12}\) (b) \(\frac{12}{13}\) (c) \(\frac{12}{5}\) (d) \(\frac{5}{13}\)

5. If \(\sin B = \frac{1}{2}\), then \(3 \cos B – 4 \cos^3 B\) is equal to (a) 1 (b) \(\frac{3}{4}\) (c) 0 (d) \(2\frac{1}{2}\)

6. If \(\sec \alpha = \frac{5}{4}\), then \(\frac{\tan \alpha}{1 + \tan^2 \alpha}\) is equal to (a) \(\frac{9}{25}\) (b) \(\frac{12}{25}\) (c) \(\frac{3}{4}\) (d) \(\frac{1}{25}\)

7. If \(3 \tan \theta = 4\), then \(\sqrt{\frac{1 – \sin \theta}{1 + \sin \theta}}\) is equal to (a) \(\frac{1}{2}\) (b) \(\frac{2}{3}\) (c) \(\frac{1}{3}\) (d) None of these

8. Find the value of \(\tan \theta + \cot \theta\). (a) \(\sin \theta\) (b) 0 (c) \(\frac{1}{\sin \theta \cos \theta}\) (d) \(\sin \theta \cos \theta\)

9. If \(\tan \theta + \frac{1}{\tan \theta} = 2\), then the value of \(\tan^2 \theta + \frac{1}{\tan^2 \theta}\) is equal to (a) 6 (b) 4 (c) 2 (d) 3

10. If \(\tan \theta = \frac{12}{13}\), then \(\frac{2 \sin \theta \cos \theta}{\cos^2 \theta – \sin^2 \theta}\) is equal to (a) \(\frac{123}{25}\) (b) \(\frac{312}{25}\) (c) \(\frac{231}{25}\) (d) \(\frac{192}{25}\)

11. The value of \(\sin^2\theta + \cos^2\theta\) is: (a) 2 (b) 1 (c) 3 (d) \(\sqrt{3}\)

12. The value of \(\frac{1 + \sec \theta}{\sec \theta}\) is: (a) \(\frac{\sin^2 \theta}{1-\cos\theta}\) (b) \(\tan \theta\) (c) \(\sec \sqrt{x}\) (d) \(\frac{\cos^2 \theta}{1-\cos\theta}\)

13. The value of \(\frac{\sec 60°+\csc 60°}{\tan 45°}\) is: (a) 1 (b) \(\frac{2\sqrt{3} + 2}{\sqrt{3}}\) (c) 2 (d) \(\frac{2\sqrt{2} + 2}{\sqrt{3}}\)

14. The value of \(\frac{\cos 90° + \sin 90°}{\cot 30°}\) is: (a) 0 (b) \(\frac{1}{2}\) (c) \(\sqrt{3}\) (d) \(\frac{1}{\sqrt{3}}\)

15. The value of \(\frac{\cos 90°+ \sin 0°}{\cot 30°}\) is: (a) \(\frac{1}{2}\) (b) 0 (c) \(\sqrt{3}\) (d) \(\frac{1}{\sqrt{3}}\)

16. The value of \(\csc 0° + \sec 90° + \tan 90°\) is: (a) \(\infty\) (b) 1 (c) \(\frac{1}{\sqrt{2}}\) (d) 0

17. The value of \(\frac{\cos \frac{\pi}{4} + \sin \frac{\pi}{4}}{\tan \frac{\pi}{4}}\) is: (a) \(\sqrt{2}\) (b) \(\frac{1}{\sqrt{2}}\) (c) 2 (d) \(\frac{1}{2}\)

18. The value of \(\sin 90° + \cos 90° + \tan 90°\) is: (a) 0 (b) \(\infty\) (c) 1 (d) \(\sqrt{3}\)

19. The value of \(\frac{\tan 30° \times \tan 60°}{\sec 60°- \sin 90°}\) is: (a) \(\frac{1}{\sqrt{3}}\) (b) 0 (c) \(\sqrt{3}\) (d) 1

20. The value of \(\sin (120°)\) is: (a) \(\frac{1}{\sqrt{2}}\) (b) \(\sqrt{3}\) (c) \(\frac{1}{2}\) (d) \(\frac{\sqrt{3}}{2}\)

21. The value of \(\cos 120°\) is: (a) \(\frac{1}{\sqrt{2}}\) (b) \(-\frac{1}{2}\) (c) \(\frac{1}{2}\) (d) 0

22. The value of \(\tan 150°\) is: (a) \(-\frac{1}{\sqrt{3}}\) (b) \(\frac{1}{\sqrt{3}}\) (c) \(\sqrt{3}\) (d) \(\frac{2}{\sqrt{3}}\)

23. What is the value of \(\csc^2 30° + \sin^2 45° + \cos^2 60°\)? (a) \(\frac{49}{32}\) (b) \(\frac{32}{81}\) (c) \(\frac{19}{4}\) (d) None of these

24. If \(\sin^2 \theta = \frac{1}{2}\) \((0° < \theta < 90°)\), then find the value of \(\theta\): (a) \(\theta = 45°\) (b) \(\theta = 60°\) (c) \(\theta = 15°\) (d) \(\theta = 30°\)

25. If \(x \tan 45° \cos 60° = \sin 60° \cot 60°\), then \(x\) equals to: (a) 1 (b) \(\frac{1}{2}\) (c) \(\sqrt{3}\) (d) \(\frac{\sqrt{2}}{2}\)