Title TRIGONOMETRIC FUNCTIONS Q-5.pdf ✅

Class : XIth Subject : MATHS Date : DPP No. : 5 1. If θ ∈ [0,5π] and r ∈ R such that 2sin θ = r 4 ― 2r 2 + 3, then the maximum number of values of the pair (r,θ) is a) 6 b)8 c) 10 d)None of these 2. In a triangle ABC, r = a) (s ― a)tan B 2 b) (s ― b)tan B 2 c) (s ― b)tan C 2 d)(s ― a)tan C 2 3. If p1,p2,p3 are altitude of a triangle ABC from the vertices A,B,C and ∆, the area of the triangle, then 1 p 2 1 + 1 p 2 2 + 1 p 2 3 = a) cotA + cosB + cot C ∆ b) ∆ cotA + cotB + cot C c) ∆(cotA + cotB + cot C) d)None of these 4. Number of solutions of the equation sin 2θ + 2 = 4 sin θ + cos θ lying in the interval [π,5 π], is a) 0 b)2 c) 4 d)5 5. If twice the square of the diameter of a circle is equal to half the sum of the squares of the sides of incribed triangle ABC, then sin2A + sin2 C is equal to a) 1 b)2 c) 4 d)8 6. tan 9° ― tan 27° ― tan 63° + tan 81° is equal to a) 0 b)1 c) ―1 d)4 7. If sin 4A ― cos 2A = cos 4A ― sin 2A, (0 < A < π 4 ), then the value of tan 4A is a) 1 b) 1 3 c) 3 d) 3 ― 1 3 + 1 8. In a ∆ABC,sinA and sinB are the roots of the equation c 2 x 2 ―c(a + b)x + ab = 0, then sin C = a) 1/ 2 b)1/2 c) 1 d)0 9. If sin(α + β) = 1,sin(α ― β) = 1 /2; α, β ∈ [0, π/2], then tan(α + 2β)tan(2α + β) is equal to a) 1 b) ―1 c) 0 d)1/2 10. If an+1 = 1 2 (1 + an ), then cos ( 1 ― a 2 0 a1a2a3...to ∞) = a) 1 b) ―1 c) a0 d)1/a0 11. If the angles of a triangle are in the ratio 1 :2 :7, then the ratio of the greatest side to the least side is a) ( 5 ― 1) :( 5 + 1) b)( 5 + 1) :( 5 ― 1) c) ( 5 + 2) :( 5 ― 2) d)( 5 ― 2) :( 5 + 2) Topic :- TRIGONOMETRIC FUNCTIONS