Introduction to Trigonometry PDF Past Papers

Introduction to Trigonometry 1 Mark: 3 1 1. If 3𝑥 = cosec 𝜃 and 𝑥 = cot 𝜃, find the value of 3 (𝑥 2 − 𝑥 2). CBSE 2010, Delhi (30/1/1)...

Introduction to Trigonometry 1 Mark: 3 1 1. If 3𝑥 = cosec 𝜃 and 𝑥 = cot 𝜃, find the value of 3 (𝑥 2 − 𝑥 2). CBSE 2010, Delhi (30/1/1) 6 1 2. If 6𝑥 = sec 𝜃 and 𝑥 = tan 𝜃, find the value of 9 (𝑥 2 − 𝑥 2). CBSE 2010, Foreign (30/2/1) 3. If sec2 𝜃 (1 + sin 𝜃)(1 − sin 𝜃) = 𝑘, then find the value of 𝑘. CBSE 2009, Outside Delhi (30/1) 1 4. If sin 𝜃 = 3, then find the value of (2 cot 2 𝜃 + 2). CBSE 2009, Delhi (30/1/1) 15 5. If sec 𝐴 = and 𝐴 + 𝐵 = 90°, find the value of cosec 𝐵. CBSE 2009, Foreign (30/2/1) 7 1 6. What is the maximum value of sec 𝜃 ? CBSE Sample Paper III 2008 3 7. If tan 𝐴 = and 𝐴 + 𝐵 = 90°, then what is the value of cot 𝐵 ? CBSE Sample Paper III 2008 4 1 cosec2 𝜃−sec2 𝜃 8. Given tan 𝜃 = , what is the value of CBSE Sample Paper I 2008 √5 cosec2 𝜃+sec2 𝜃 5 9. If tan 𝐴 = , find the value of (sin 𝐴 + cos 𝐴) sec 𝐴. CBSE 2008, Foreign (30/2/1), (30/2/3) 12 7 10. If cos 𝐴 = 25, find the value of tan 𝐴 + cot 𝐴. CBSE 2008, Foreign (30/2/2) 2 Marks : 1. Without using trigonometric tables, find the value of the following expression: sec(90°−𝜃).cosec 𝜃−tan(90°−𝜃) cot 𝜃+cos2 25°+cos2 65° CBSE 2010, Delhi (30/1/1) 3 tan 27°.tan 63° 2. Find the value of cosec 30°, geometrically. CBSE 2010, Delhi (30/1/1) 3. Without using trigonometric tables, find the value of the following: CBSE 2010, Foreign (30/2/1) cot 𝜃. tan(90° − 𝜃) − sec(90° − 𝜃) cosec 𝜃 + √3. tan 12°. tan 60°. tan 78° 4. Find the value of sec 45° geometrically. CBSE 2010, Foreign (30/2/1) sin3 𝜃+cos3 𝜃 5. Simplify : + sin 𝜃 cos 𝜃 CBSE 2009, Delhi (30/1/1) sin 𝜃+cos 𝜃 15 (2+2 sin 𝜃)(1−sin 𝜃) 6. If cot 𝜃 = , then evaluate. CBSE 2009, Outside Delhi (30/1) 8 (1+cos 𝜃)(2−2 cos 𝜃) 7. Find the value of tan 60°, geometrically. CBSE 2009, Outside Delhi (30/1) 8. Without using trigonometric tables, evaluate: 7 cos 70° 3 cos 55° cosec 35° + 2 tan 5° tan 25° tan 45° tan 85° tan 65° CBSE 2009, Foreign (30/2/1) 2 sin 20° 9. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45° CBSE Sample Paper II 2008 10. If 𝐴, 𝐵, 𝐶 are interior angles of Δ𝐴𝐵𝐶, then show that 𝐵+𝐶 𝐴 cos ( ) = sin 2 CBSE Sample Paper II 2008 2 cos 70° 11. Without using trigonometric tables, find the value of sin 20° + cos 57° cosec 33° − 2 cos 60° CBSE Sample Paper I 2008 12. If sec 4𝐴 = cosec(𝐴 − 20°), where 4𝐴 is an acute angle, find the value of 𝐴. CBSE 2008, Foreign (30/2/1), (30/2/3)  1 13. In a Δ𝐴𝐵𝐶, right-angled at 𝐶, if tan 𝐴 = , find the value of √3 sin 𝐴 cos 𝐵 + cos 𝐴 sin 𝐵 CBSE 2008, Foreign (30/2/1), (30/2/3) 14. If sec 2𝐴 = cosec(𝐴 − 42°), where 2𝐴 is an acute angle, find the value of 𝐴. CBSE 2008, Foreign (30/2/2) 15. In Δ𝐴𝐵𝐶, right angled at 𝐴, if tan 𝐶 = √3, find the value of sin 𝐵 cos 𝐶 + cos 𝐵 sin 𝐶. CBSE 2008, Foreign (30/2/2) 3 Marks: 1. Prove the following: tan 𝐴 cot 𝐴 1−cot 𝐴 + 1−tan 𝐴 = 1 + tan 𝐴 + cot 𝐴 CBSE 2010, Delhi (30/1/1) 2. Prove the following: 1 (cosec 𝐴 − sin 𝐴)(sec 𝐴 − cos 𝐴) = CBSE 2010, Delhi (30/1/1) tan 𝐴+cot 𝐴 2 2 3. If tan 𝜃 + sin 𝜃 = 𝑚 & tan 𝜃 − sin 𝜃 = 𝑛, show that 𝑚 − 𝑛 = 4√𝑚𝑛. CBSE 2010, Foreign (30/2/1) 4. Show that: 1 1 1 (1 + ) (1 + )=. CBSE 2010, Foreign (30/2/1) tan2 𝜃 cot2 𝜃 sin2 𝜃−sin4 𝜃 5. Find the value of sin 30° geometrically. CBSE 2009, Delhi (30/1/1) 6. Without using trigonometrical tables, evaluate: cos 58° sin 22° cos 30° cosec 52° sin 32° + cos 68° − tan 18° tan 35° tan 60° tan 72° tan 55° CBSE 2009, Delhi (30/1/1) 7. Prove that sin2 𝜃−2 sin4 𝜃 sec 2 𝜃 − 2 cos4 𝜃−cos2 𝜃 = 1 CBSE 2009, Foreign (30/2/1) 8. Evaluate: 2 2 5 cosec2 58° − cot 58° tan 32° − tan 13° tan 37° tan 45° tan 53° tan 77° 3 3 3 CBSE 2009, Outside Delhi (30/1) 9. Prove that: (1 + cot 𝐴 + tan 𝐴)(sin 𝐴 − cos 𝐴) = sin 𝐴 tan 𝐴 − cot 𝐴 cos 𝐴. CBSE 2008, Foreign (30/2/1), (30/2/2), (30/2/3) 10. Without using trigonometric tables, evaluate the following: cos 58° cos 38° cosec 52° 2 ( sin 32° ) − √3 (tan 15° tan 60° tan 75°) CBSE 2008, Foreign (30/2/1), (30/2/2), (30/2/3) 11. Prove that sin 𝜃 sin 𝜃 = 2 + cot 𝜃−cosec 𝜃 CBSE Sample Paper III 2008 cot 𝜃+cosec 𝜃 12. Evaluate sec 29° + 2 cot 8° cot 17° cot 45° cot 73° cot 82° − 3(sin2 38° + sin2 52°) CBSE Sample Paper III 2008 cosec 61° 13. Prove that sec 𝐴−1 sec 𝐴+1 √sec 𝐴+1 + √sec 𝐴−1 = 2 cosec 𝐴 CBSE Sample Paper II 2008 1+cos 𝐴 sin 𝐴 14. Prove that: + 1+cos 𝐴 = 2 cosec 𝐴 CBSE Sample Paper I 2008 sin 𝐴 sin 𝐴+cos 𝐴 sin 𝐴−cos 𝐴 2 15. Prove that: sin 𝐴−cos 𝐴 + sin 𝐴+cos 𝐴 = sin2 𝐴−cos2 𝐴 CBSE Sample Paper I 2008