Tiêu đề TRIGONOMETRIC FUNCTIONS Q-10.pdf ✅

Class : XIth Subject : MATHS Date : DPP No. : 10 1. The greatest and least value of sin x cos x are respectively a) 1, ―1 b) 1 2 , ― 1 2 c) 1 4 , ― 1 4 d)2, ―2 2. If x = Xcos θ ― Y sin θ,y = X sin θ + Y cos θ and x 2 +4x y + y 2 = AX 2 +BY 2 , 0 ≤ θ ≤ π 2 ,n ∈ Z, then a) θ = π 6 ,A = 3,B = 1 b)θ = π 2 ,A = 3,B = 1 c) A = 3,B = ―1,θ = π 4 d)A = ―3,B = 1,θ = π 4 3. The number of values of x in [0, 2π] satisfying the equation 3cos 2x ― 10 cos x + 7 = 0 is a) 1 b)2 c) 3 d)4 4. cosα sin(β ― γ) + cosβ sin(γ ― α) + cos γ sin(α ― β) is equal to a) 0 b) 1 2 c) 1 d)4cosα cosβ cos γ 5. If A + B = 45°, then (cotA ― 1)(cotB ― 1) is equal to a) 1 b) 1 2 c) ―1 d)2 6. The solution of the equation [sin x + cos x] 1+sin 2x = 2, ―π ≤ x ≤ π is a) π 2 b)π c) π 4 d)3π 4 7. If sin x + sin2 x = 1, then the value of cos12 x +3cos10 x +3cos8 x + cos6 x +2cos4 x + cos2 x ―2, is equal to a) 0 b)1 c) 2 d)sin2 x 8. sin4 π 8 + sin4 3π 8 + sin4 5π 8 + sin4 7π 8 is equal to a) 1 b)3/2 c) 2 d)1 /4 9. If sin(x + 3α) = 3 sin(α ― x), then a)tan x = tanα b)tan x = tan2α c) tan x = tan3α d)tan x = 3 tanα 10. cosαsin(β ― γ) + cosβsin(γ ― β) + cos γsin(α ― β) = a) 0 b)1/2 c) 1 d)4cosαcosβcos γ 11. If sinA + cosA = m and sin3A + cos3A = n, then a) m3 ―3m + n = 0 b)n 3 ―3n + 2m = 0 c) m3 ―3m + 2n = 0 d)m3 +3m + 2n = 0 12. If (sec θ ― 1) = ( 2 ― 1)tan θ, then θ = a) n π + π 8 ,n ∈ Z b)2 n π,2 n π + π 4 ,n ∈ Z c) 2 n π,n ∈ Z d)None of these 13. The number of values of θ in the interval [ ― π, π] satisfying the equation cos θ + sin 2θ = 0 is a) 1 b)2 c) 3 d)4 Topic :- TRIGONOMETRIC FUNCTIONS