SECTION B — Very Short Answer Type Questions [2 Marks Each]
- 2 Marks Q26. Show that: $\cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ = 0$.
- 2 Marks Q27. If $\tan 2A = \cot(A - 18^\circ)$, where $2A$ is an acute angle, find the value of $A$.
- 2 Marks Q28. If $\sec 4A = \csc(A - 20^\circ)$, where $4A$ is an acute angle, find the value of $A$
- 2 Marks Q29. If $A, B$ and $C$ are interior angles of a triangle $ABC$, then show that $\sin\left(\frac{B + C}{2}\right) = \cos\left(\frac{A}{2}\right)$.
- 2 Marks Q30. Express $\sin 67^\circ + \cos 75^\circ$ in terms of trigonometric ratios of angles between $0^\circ$ and $45^\circ$.
- 2 Marks Q31. If $\sin A = \cos(A - 26^\circ)$, where $3A$ is an acute angle, find the value of $A$.
- 2 Marks Q32. If $\cos(2A) = \sin(A - 15^\circ)$, where $2A$ is an acute angle, find $A$.
- 2 Marks Q33. Find the value of: $\frac{\sin 35^\circ}{\cos 55^\circ} + \frac{\cos 55^\circ}{\sin 35^\circ} - 2\cos^2 60^\circ$.
- 2 Marks Q34. Evaluate: $\frac{\tan 50^\circ + \sec 50^\circ}{\cot 40^\circ + \csc 40^\circ}$
- 2 Marks Q35. If $\tan A = \cot B$, prove that $A + B = 90^\circ$.
- 2 Marks Q36. Express the trigonometric ratios $\sin A$, $\sec A$ and $\tan A$ in terms of $\cot A$.
- 2 Marks Q37. Write all the other trigonometric ratios of $\angle A$ in terms of $\sec A$.
- 2 Marks Q38. Prove that: $(\sec A - \tan A)(1 + \sin A) = \cos A$.
- 2 Marks Q39. Prove that: $\frac{1 + \sec A}{\sec A} = \frac{\sin^2 A}{1 - \cos A}$.
- 2 Marks Q40. Prove that: $\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + \tan A$
- 2 Marks Q41. Simplify: $(1 - \cos\theta)(1 + \cos\theta)(1 + \cot^2\theta)$
- 2 Marks Q42. Prove that: $\sin\theta - 2\sin^3\theta = 2\cos^3\theta - \cos\theta$.
- 2 Marks Q43. Prove that: $(\sin A + \csc A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A$.
- 2 Marks Q44. Prove that: $\frac{\sin\theta - 2\sin^3\theta}{2\cos^3\theta - \cos\theta} = \tan\theta$.
- 2 Marks Q45. If $\sec \theta + \tan \theta = m$, find the value of $\sec \theta - \tan \theta$.
- 2 Marks Q46. If $\sin \theta + \cos \theta = \sqrt{2}\cos \theta$, show that $\cos \theta - \sin \theta = \sqrt{2}\sin \theta$.
- 2 Marks Q47. Prove that: $\frac{\tan\theta}{1 - \cot\theta} + \frac{\cot\theta}{1 - \tan\theta} = 1 + \sec\theta \csc\theta$.
- 2 Marks Q48. Prove that: $\frac{1 + \tan^2 A}{1 + \cot^2 A} = \left(\frac{1 - \tan A}{1 - \cot A}\right)^2 = \tan^2 A$.
- 2 Marks Q49. Prove the identity: $\frac{\cos A}{1 - \tan A} + \frac{\sin A}{1 - \cot A} = \sin A + \cos A$
- 2 Marks Q50. If $x = a \sec \theta + b \tan \theta$ and $y = a \tan \theta + b \sec \theta$, prove that $x^2 - y^2 = a^2 - b^2$.
Academic Repository Disclaimer & எச்சரிக்கை அறிவிப்பு :
English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.
தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.
Copyright © 2026 Deepa Maths Academy | Global Examination & Academic Portal. All Rights Reserved.