If cos θ+cos 2θ+ cos 3θ=0 then θ=
(2n+1) π/4: n ε Z or 2nπ ±2 π/3: n ε Z
nπ/4: n ε Z or nπ ± π/6: n ε Z
nπ: n ε Z or (2n+1) π/9: n ε Z
(2n+1) π/10: n ε Z or 2nπ/3± π/9: n ε Z
If 4 cos θ.cos (1200+ θ). Cos (1200- θ)=1/2 then θ=
nπ or (3n ±1)π/9: n ε Z
nπ/3 + (-1)nπ/6: n ε Z
2nπ/3 ± π/9: n ε Z
nπ/3 + π/18: n ε Z
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=
π/4
π/3
π/2
π/6
If cot θ+ cosec θ= √3 then θ=
2nπ + π/6
2nπ + π/3
2nπ - π/6
none of these
If tan (π/2 sin θ) = cot (π/2 cos θ) then sin (θ+ π/4) =
±1/2
± 1/√2
± 1/2√2
2
If 6 Sec2 θ-5 Sec θ+1=0 then θ=
nπ ± 5π/6
2nπ ± 5π/6
nπ ± 3π/4
2nπ ± 3π/4
If tan θ + tan 2θ+ √3 tan θ tan 2θ=√3 then θ=
(nπ/3) + (π/9): n ε Z
(nπ/3) + (π/12): n ε Z
(nπ/3) + (-1)n (π/6): n ε Z
nπ +π/4: n ε Z
If α,β are the roots of ax2+bx+c=0 then α2/β+β2/α=
3abc-b3/a3
3abc-b3/a2c
b2-2ac/c2
b2-2ac/ac
If tan2 θ=3 cosec2 θ-1 then θ=
nπ ± π/3: n ε Z
nπ + π/4: n ε Z
nπ+ (-1)nπ/6: n ε Z
nπ - π/3: n ε Z
The solution of sin 2θ+cos 2θ+sin θ+ cos θ+1=0 in the first quadrant is
2nπ: n ε Z or (2n-1)π+π/6: n ε Z
(2n+1)π/2: n ε Z r nπ-π/4: n ε Z
2nπ+π/2: n ε Z
No solution
The equation cos4x-(a+2)cos2x-(a+3) =0 possesses a solution if
a>-3
a
-3 ≤ a ≤-2
a is any positive integer
If cos θ=cos 5π/4, then θ=
2nπ±π/4
2nπ±3π/4
2nπ±5π/4
2nπ±7π/4
The smallest positive values of x and y which satisfy tan(x-y) =1, sec(x+y) = 2/√3 are
x=25π/24, y=19π/24
x=7π/24, y=37π/24
x=π/4, y=π/2
x=π/3, y=7π/12
If sin θ=-7/25 and is not in the first quadrant, then (7cot θ -24 tan θ) / (7cot θ+24 tan θ) =
17/31
-17/31
31/17
-31/17
If sin 7θ+sin 4θ+ sin θ=0, 0≤θ≤ π/2 then θ=
0, π/2, π, 3π/5
0, π/3, π, 2π/3
0, π/4, π/2, 2π/9
1, π/2, π, 2π/9
If tan x+ tan 4x+tan 7x=tan x tan 4x tan 7x, then x=
nπ/3
nπ/4
nπ/6
nπ/12
The domain of Cos-1 (4x-9) is
(2, 5/2)
[5/2]
(9/4, π+9/4)
If 4 sin x.sin 2x.sin 4x=sin 3x then x=
nπ or (3n±1)π/9: n ε Z
nπ/3 + (-1)n π/6: n ε Z
If 2 Sin2x + √3 Cosx+1=0, then θ=
2 nπ ± 5π/6
If tan θ+ tan 2θ+tan 3θ= 0 then θ=
nπ/3: n ε Z or nπ±tan-1(1/√2): n ε Z
nπ/3+ (-1)nπ/6: n ε Z
(4n+1)π/12: n ε Z
If cos θ+√3 sinθ=2 then θ=
2π/3
4π/3
5π/3
If sin A=sin B and cos A=cos B then A=
2nπ+B
2nπ-B
nπ+B
nπ+(-1)nB
If 2Sin2 θ=3 Cos θ, then the valueof θ in [0,2π] are
π/3, 2π/3
π/3, 5π/3
2π/3, 5π/3
none
All the values of x satisfying sin 2x+ sin 4x= 2 sin 3x are
2nπ
nπ
nπ + π/3
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
[-1/2, 1]
[1/2, ∞)
[1, 2)
[1, ∞)
If sin x-3 sin 2x+sin 3x=cos x-3cos 2x+cos 3x then x=
nπ + π/8
nπ/2 + π/8
(-1)2nπ/2+ π/8
2nπ+cos -13/2
If 2-cos3 θ=3 sin θ cos θ then θ=
nπ +π/3: n ε Z
nπ + tan-1(1/2): n ε Z or nπ+π/4: n ε Z
nπ + (-1)nπ/6: n ε Z
nπ + tan-1(3/2): n εZ or nπ+ tan-1(1/4): n ε Z
The solution set of sec θ=2cos θ is
{nπ ± π/3: n ε Z}
{nπ ± π/4: n ε Z}
{nπ ± π/6: n ε Z}
{nπ ± n: n ε Z}
If x is an acute angle and sin(x+280) =cos (3x-780), then x=
2480or 1120
350 or 80
460 or 70
2650 or 1190
If tan A,tan B are the roots of x2-px+q=0,the value of sin2(A+B) is
p2/p2+(1-q)2
p2/p2+q2
q2/p2+(1-q)2
p2/(p+q)2