If sin 7θ+sin 4θ+ sin θ=0, 0≤θ≤ π/2 then θ=
A. 0, π/2, π, 3π/5
B. 0, π/3, π, 2π/3
C. 0, π/4, π/2, 2π/9
D. 1, π/2, π, 2π/9
If α,β are the roots of ax2+bx+c=0 then α2/β+β2/α=
A. 3abc-b3/a3
B. 3abc-b3/a2c
C. b2-2ac/c2
D. b2-2ac/ac
If 2Sin2 θ=3 Cos θ, then the valueof θ in [0,2π] are
A. π/3, 2π/3
B. π/3, 5π/3
C. 2π/3, 5π/3
D. none
The domain of sin-1(2x-7) is
A. (3, 4)
B. [3, 4]
C. [-π/4 + 7/2, π/4 + 7/2]
D. [-π/4 + 7/2, π/4 + 7/2]
If the sum of the squares of the roots of the equation x2-(sin α-2)x-(1+sin α)=0 is least,then α=
A. π/4
B. π/3
C. π/2
D. π/6
The general solution of sin2 θ sec θ+ √3tan θ=0 is
A. θ=nπ+(-1)n+1π/3,θ=nπ, n ε Z
B. θ=nπ, n ε Z
C. θ=nπ+(-1)n+1π/3,n ε Z
D. θ= nπ/2, n ε Z
If tan θ + tan 2θ+ √3 tan θ tan 2θ=√3 then θ=
A. (nπ/3) + (π/9): n ε Z
B. (nπ/3) + (π/12): n ε Z
C. (nπ/3) + (-1)n (π/6): n ε Z
D. nπ +π/4: n ε Z
If α, β, γ are the angles made by a line with x, y, z axes in positive directions then the range of cos α cos β+ cos β cos γ+cos γ cos α is
A. [-1/2, 1]
B. [1/2, ∞)
C. [1, 2)
D. [1, ∞)
If tan θ+tan (600+θ) tan (1200+θ) =3, then θ=
A. (4n+1) π/12
B. (2n+1) π/12
C. nπ + π/3
D. none
If sin θ=-7/25 and is not in the first quadrant, then (7cot θ -24 tan θ) / (7cot θ+24 tan θ) =
A. 17/31
B. -17/31
C. 31/17
D. -31/17
If tan A,tan B are the roots of x2-px+q=0,the value of sin2(A+B) is
A. p2/p2+(1-q)2
B. p2/p2+q2
C. q2/p2+(1-q)2
D. p2/(p+q)2
The equation cos4x-(a+2)cos2x-(a+3) =0 possesses a solution if
A. a>-3
B. a
C. -3 ≤ a ≤-2
D. a is any positive integer
If 4 sin x.sin 2x.sin 4x=sin 3x then x=
A. nπ or (3n±1)π/9: n ε Z
B. nπ/3 + (-1)n π/6: n ε Z
C. 2nπ/3 ± π/9: n ε Z
D. nπ/3 + π/18: n ε Z
If sin x-3 sin 2x+sin 3x=cos x-3cos 2x+cos 3x then x=
A. nπ + π/8
B. nπ/2 + π/8
C. (-1)2nπ/2+ π/8
D. 2nπ+cos -13/2
If cos θ+cos 2θ+ cos 3θ=0 then θ=
A. (2n+1) π/4: n ε Z or 2nπ ±2 π/3: n ε Z
B. nπ/4: n ε Z or nπ ± π/6: n ε Z
C. nπ: n ε Z or (2n+1) π/9: n ε Z
D. (2n+1) π/10: n ε Z or 2nπ/3± π/9: n ε Z
If tan (π/2 sin θ) = cot (π/2 cos θ) then sin (θ+ π/4) =
A. ±1/2
B. ± 1/√2
C. ± 1/2√2
D. 2
If cos 2θ+cos 8θ= cos 5θ then θ=
A. (2n+1) π/4 : n ε Z or 2n π ± 2 π/3: n ε Z
B. nπ/4: n ε Z or nπ ± π/6: n ε Z
C. nπ: n ε Z or (2n+1) π/9: n ε Z
D. (2n+1) π / 10: n ε Z or 2nπ/3 ± π / 9: n ε Z
If 2-cos3 θ=3 sin θ cos θ then θ=
A. nπ +π/3: n ε Z
B. nπ + tan-1(1/2): n ε Z or nπ+π/4: n ε Z
C. nπ + (-1)nπ/6: n ε Z
D. nπ + tan-1(3/2): n εZ or nπ+ tan-1(1/4): n ε Z
The solution of sin 2θ+cos 2θ+sin θ+ cos θ+1=0 in the first quadrant is
A. 2nπ: n ε Z or (2n-1)π+π/6: n ε Z
B. (2n+1)π/2: n ε Z r nπ-π/4: n ε Z
C. 2nπ+π/2: n ε Z
D. No solution
The solution set of sec θ=2cos θ is
A. {nπ ± π/3: n ε Z}
B. {nπ ± π/4: n ε Z}
C. {nπ ± π/6: n ε Z}
D. {nπ ± n: n ε Z}
If tan2 θ=3 cosec2 θ-1 then θ=
A. nπ ± π/3: n ε Z
B. nπ + π/4: n ε Z
C. nπ+ (-1)nπ/6: n ε Z
D. nπ - π/3: n ε Z
If tan (cot x) = cot (tan x), then sin 2x=
A. (2n+1) π/4
B. 4/ (2n+1) π
C. 4π/ (2n+1)
D. none
If 4 cos θ.cos (1200+ θ). Cos (1200- θ)=1/2 then θ=
A. nπ or (3n ±1)π/9: n ε Z
B. nπ/3 + (-1)nπ/6: n ε Z
C. 2nπ/3 ± π/9: n ε Z
D. nπ/3 + π/18: n ε Z