Title TRIGONOMETRIC FUNCTIONS Q-3.pdf ✅

Class : XIth Subject : MATHS Date : DPP No. : 3 1. In a ∆ABC, angles A,B,C are in A.P., then lim A→C 3 ― 4 sinA sinC |A ― C| is equal to a) 1 b)2 c) 3 d)4 2. For all values of θ, the values of 3 ― cos θ + cos (θ + π 3 ) lie in the interval a)[ ― 2, 3] b)[ ― 2, 1] c) [2, 4] d)[1, 5] 3. If cosA = m cosB and cot A + B 2 = λ tan B ― A 2 , then λ is a) m m ― 1 b) m + 1 m c) m + 1 m ― 1 d)None of these 4. The value of cos4 ( π 8 ) + cos4 ( 3π 8 ) + cos4 ( 5π 8 ) + cos4 ( 7π 8 ) is a) 0 b) 1 2 c) 3 2 d)1 5. If sin θ = 12 13 , (0 < θ < π 2 ) and cos φ = ― 3 5 (π < φ < 3 π 2 ), then sin(θ + φ) will be a) ―56/61b) ―56/65c) 1/65d) ―56 6. The quadratic equation whose roots are sec2 θ and cosec 2 θ can be a) x 2 ―2x + 2 = 0 b)x 2 +5x + 5 = 0 c) x 2 ―4x + 4 = 0 d)None of these 7. If sec θ = m and tan θ = n, then 1 m [(m + n) + 1 (m + n)] is a) 2 b)2m c) 2n d)mn 8. If in a ∆ ABC, ∠C = 90°, then the maximum value of sinA sinB is a) 1 2 b)1 c) 2 d)None of these 9. In a cyclic quadrilateral ABCD, he value of cosA + cosB + cos C + cosD, is a) 1 b)0 c) ―1 d)None of these 10. If the angles of a triangle are in the ratio 1 :2 :3, the corresponding sides are in the ratio a) 2 :3 :1 b) 3 :2 :1 c) 2 : 3 :1 d)1 : 3 :2 11. If sin(π cos θ ) = cos(π sin θ), then the value of cos (θ + π 4 ) equals a) 1 2 b) 1 2 2 c) ― 1 2 2 d) ― 1 2 12. The most general solution of 2 1+|cos x|+cos2 x+|cos3 x|+...∞ = 4 is given by a) x = nπ ± π 3 ,n ∈ Z b)x = 2n π ± π 3 ,n ∈ Z c) x = 2n π ± 2π 3 ,n ∈ Z d)None of these Topic :- TRIGONOMETRIC FUNCTIONS