M0IITU04 - Trigo eqns &amp; prop of triangles qns

# M0IITU04 - Trigo eqns &amp; prop of triangles qns -...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. If sin θ + cos θ = 1, then the general value of θ is : (A) 2 n π (B) n π + (- 1) n π π 4 4 - (C) 2 n π + π 2 (D) None of these 2. If sec 2 θ = 4 3 , then the general value of θ is : (A) 2 n π ± π 6 (B) n π ± π 6 (C) 2 n π ± π 3 (D) n π ± π 3 3. If 2 cos 2 x + 3 sin x - 3 = 0, 0 x 180º, then x = (A) 30º, 90º, 150º (B) 60º, 120º, 180º (C) 0º, 30º, 150º (D) 45º, 90º, 135º 4. If sin 2 θ - 2 cos θ + 1 4 = 0, then the general value of θ is : (A) n π ± π 3 (B) 2 n π ± π 3 (C) 2 n π ± π 6 (D) n π ± π 6 4. The most general value of θ satisfying the equations, tan θ = - 1 cos θ = 1 2 is : (A) n π + 7 4 π (B) n π + ( - 1) n 7 4 π (C) 2 n π + (D) None of these 6. If tan 2 θ tan θ = 1. then then general value of θ is : (A) n + 1 2 π 3 (B) n + 1 2 π (C) 2 1 2 n ± π 3 (D) None of these 7. If sin 5x + sin 3x + sin x = 0, then the value of x other than 0 lying between 0 x π 2 is : (A) π 6 (B) π 12 (C) π 3 (D) π 4 8. If cot θ + tan θ = 2 cosec θ , the general value of θ is : (A) n π ± π 3 (B) n π ± π 6 (C) 2 n π ± π 3 (D) 2 n π ± π 6 9. If 2 sin 2 θ = 3 cos θ , where 0 ≤ θ ≤ 2 π , then θ = (A) π π 6 7 6 , (B) π π 3 5 3 , (C) π π 3 7 3 , (D) None of these 10. If sec x cos 5x + 1 = 0, where 0 < x < 2 π , then x = Trigonometry Equations & Properties

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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 (A) π π 5 4 , (B) π 5 (C) π 4 (D) None of these 11. If sec 4 θ - sec 2 θ = 2, then the general value of θ is : (A) (2n + 1) π 4 (B) (2n + 1) π 10 (C) n π + π 2 or n π 5 + π 10 (D) None of these 12. In a triangle ABC, a = 5, b = 7 and sin A = 3 4 , how many such triangles are possible ? (A) 1 (B) 0 (C) 2 (D) Infinite 13. Peroid of sin 2x is : (A) π 4 (B) π 2 (C) π (D) 2 π 14. Peroid of sin θ - 3 cos θ is : (A) π 4 (B) π 2 (C) π (D) 2 π 15. If in a Δ ABC, (s - a) (s - b) = s (s - c), then angle C is equal to : (A) 90º (B) 45º (C) 30º (D) 60º 16. In triangle ABC, b c a + = (A) cos ( ) sin 1 2 1 2 B C A - (B) sin ( ) cos 1 2 1 2 B C A - (C) cos ( ) sin 1 2 1 2 B C A + (D) cos ( ) cos 1 2 1 2 B C A + 17. In Δ ABC if, cosA a = cosB b = cosC c , then the triangle is : (A) Right angled (B) Obtuse angled (C) Equilateral (D) Isosceles 18. In triangle ABC, sin ( ) sin ( ) A B A B - + = (A) a b c 2 2 2 - (B) a b c 2 2 2 + (C) c a b 2 2 2 - (D) c a b 2 2 2 + 19. In a triangle ABC, if b 2 + c 2 = 3 a 2 , then cot B + cot C - cot A = (A) 1 (B) a b 4 Δ (C) 0 (D) a c 4 Δ 20. In triangle ABC, cot cot A B 2 2 + a B b A sin sin 2 2 2 2 + = (A) cot C (B) c cot C (C) cot C 2 (D) c cot C 2 21. In a triangle ABC, if 3a = b + c, then the value of cot B 2 cot C 2 is : (A) 1 (B) 2
3 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439

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## This note was uploaded on 10/05/2011 for the course MATH 1201 taught by Professor Friesner during the Spring '11 term at St. Mary NE.

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M0IITU04 - Trigo eqns &amp; prop of triangles qns -...

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