Eamcet - Maths - Trigonometric Equations

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

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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

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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

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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]

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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

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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

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If sin A=sin B and cos A=cos B then A=

A.  2nπ+B

B.  2nπ-B

C.  nπ+B

D.  nπ+(-1)nB

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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

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If y=tan x cot 3x,xR,then

A.  1/3 < y < 1

B.  1/3 ≤ y ≤ 1

C.  1/3 ≤ y ≤ 3

D.  none

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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, ∞)

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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

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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

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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

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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

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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

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If tan (πcos x) = cot (π sinx) then cos(x-π/4) =

A.  ± 1/2

B.  ± 1/√2

C.   ± 1/2√2

D.  2

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If 6 Sec2 θ-5 Sec θ+1=0 then θ=

A.  nπ ± 5π/6

B.  2nπ ± 5π/6

C.  nπ ± 3π/4

D.  2nπ ± 3π/4

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If cot θ - tan θ= sec θ, then θ =

A.  nπ + (-1)n π/6

B.   nπ + π/2

C.  2nπ + 3π/2

D.  none

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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

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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

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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

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If tan x+ tan 4x+tan 7x=tan x tan 4x tan 7x, then x=

A.  nπ/3

B.  nπ/4

C.  nπ/6

D.  nπ/12

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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

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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

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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

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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}

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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

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The domain of Cos-1 (4x-9) is

A.  (2, 5/2)

B.  [5/2]

C.  (9/4, π+9/4)

D.  (9/4, π+9/4)

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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

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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

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