### Eamcet - Maths - Inverse Trigonometric Functions

The value of Cot [Cot-1 7+ Cot-1 8+ Cot-1 (18)] is

A.  4

B.  5

C.  6

D.  3

The number of real solutions of Tan1 x+Tan 1 (1/y) = Tan1 3 is

A.  (1,4)

B.  (4,13)

C.  (2,1)

D.  none of these

Cot-1(4/3)-Cos-1(15/8) =

A.  Cot-1(16/65)

B.  Cot-1(84/65)

C.  Cot-1(84/85)

D.  Cot-1(84/13

The equation Sin-1 x- Cos-1 x=Cos-1 (√3/2) has

A.  no solution

B.  unique solution

C.  infinite number of solutions

D.  none

4 Tan-1 1/5- Tan-1 1/239 =

A.  π

B.  π/2

C.  π/4

D.  3π/4

The domain of Cosh-1 3x is

A.  R

B.  [0, ∞)

C.  [1/3, ∞)

D.  (-1/3, 1/3)

The ascending order of A= Sin-1(sin 8π/7),B= Cos-1(cos 8π/7), ), C=Tan-1(tan 8π/7) is

A.  B,A, C

B.   B,C,A

C.  A,B,C

D.  A,C,B

Cos-1(63/65) + 2 Tan-1(1/5) =

A.  Tan-1(27/11)

B.  Tan-1(16/63)

C.   Sin-1(16/65)

D.  Sin-1(3/5)

Tan-1 2+ Tan-1 3 =

A.  3π/4

B.  π/2

C.  π/4

D.   π

Let Then which one of the following is true

A.  I < 2/3 and J > 2

B.  I < 2/3 and J < 2

C.  I > 2/3 and J > 2

D.  I < 2/3 and J > 2

If cos-1(3/5) - sin-1(4/5) = cos-1(x), then x

A.  0

B.  -1

C.  1

D.  π /2

If Cos-1 x= Tan-1 x, then sin(Cos-1 x)=

A.  x

B.  x2

C.  1/x

D.  1/ x2

If Tan-1 (sec x + tan x)=π/4+kx then k=

A.  2

B.  4

C.  1/2

D.  1/4

The domain of Cos-1 (2/2+sinx) in [0,2π] is

A.  [0,π)

B.  [0, π/2]

C.  [-2,-1] U[1,2]

D.  none

Sin-1(3/5)+Sin-1(8/17)=

A.  Sin-1(56/65)

B.  Sin-1(33/65)

C.  Sin-1(77/85)

D.  Sin-1(3/5)

If Tan-1(x+1/x-1)+Tan-1(x-1/x)+ Tan-1(1/3), then x=

A.  2

B.  -2

C.  1

D.  No solution

Tan (tan-1 1/2+ tan-11/3) =

A.  1

B.  2

C.   4

D.  5

The range of f(x)= Sin-1x-cos-1x + Tan-1x is

A.  (0, π)

B.  (π/4, 3π/4)

C.  (-π/4, π/4)

D.  [0, 3π/4]

If Tan-1(x-1/x-2)+ Cot-1 (x+2/x+1)=π/4, then x=

A.  1/√2

B.  ±1/√2

C.  ±1/√3

D.  1/√3

The domain of f(x)=Tan-1 √x(x+3) + sin-1√x2+3x+1 is

A.  (-3, 0)

B.  (3, 0)

C.  {-3, 0}

D.  {0, 3}

Sin-1(-√2/2) + Cos-1(-1/2)-Tan-1(-√3)-Cot-1(1/√3) =

A.  5π/6

B.  5π/12

C.  7π/12

D.  7π/6

Sec-1√34/5+ Cosec-1√17 =

A.  π

B.  π/2

C.  π/4

D.  3π/4

Tan [cos-1 4/5+tan-1 2/3] =

A.  11/6

B.   13/6

C.  17/6

D.  none

If Sec-1(x/a)- Sec-1(x/b)= Sec-1 b- Sec-1a then x=

A.  ab

B.  b/a

C.  a/b

D.  1/ab

Sin-1(sin 2π/3) =

A.  π/12

B.  π/3

C.  3π/4

D.  π/6

sin-1(2cos2 x-1)cos-1(1-2sin2 x)

A.  π/2

B.  π/3

C.  π/4

D.   π/6

4 Tan-1 1/5- Tan-1 1/70+Tan-1 1/99 =

A.  π

B.  π/2

C.  π/4

D.  3π/4

Tan (π/4+1/2cos-1a/b) +tan (π/4-1/2cos-1a/b) =

A.  b/a

B.  a/b

C.  2a/b

D.  2b/a

If 2Tan-1(cos x) = Tan-1(2 cosec x) then x=

A.  π/4

B.  π/6

C.  π/2

D.  No solution

Tan-1 1/3+ Tan-1 1/5+ Tan-1 1/7+ Tan-1 1/8 =

A.  π

B.  π/2

C.  π/4

D.  3π/4