Find the principal value of

Find the principal value of sin⁻¹(−1/2).

Find the principal value of cos⁻¹(√3/2).

ind the principal value of

Find the principal value of cosec⁻¹(2)

Find the principal value of cosec⁻¹(2).

Find the principal value of  

Find the principal value of tan⁻¹(-√3).

Find the principal value of

Find the principal value of cos⁻¹(-1/2).

Find the principal value of tan⁻¹(-1).

Find the principal value of tan⁻¹(-1)

Find the principal value of sec⁻¹( )

Find the principal value of sec⁻¹(2/√3).

Find the principal value of cot⁻¹( )

Find the principal value of cot⁻¹(√3).

Find the principal value of cos⁻¹( )

Find the principal value of cos⁻¹(-1/√2).

Find the principal value of cosec⁻¹( )

Find the principal value of cosec⁻¹(-√2).

Find the value of 

Find the value of tan⁻¹(1) + cos⁻¹(-1/2) + sin⁻¹(-1/2).

Find the value of

Find the value of cos⁻¹(1/2) + 2sin⁻¹(1/2).

If sin^-1 x = y, then

(A) 0 ≤ y < π            (B) – π/2 ≤ y ≤ π/2            

(C) 0 < y < π            (D) – π/2 < y < π/2

If sin^-1 x = y, then

(A) 0 ≤ y < π        

(B) –  ≤ y ≤             

(C) 0 < y < π           

(D) – < y <

tan^-1 √3 – sec^-1(-2) is equal to

(A) π                                    (B) – π/3                             

(C) π/3                                (D) 2π/3

  is equal to

 (A) π                             

(B) –                         

(C)                

(D)

Prove that 3sin^-1 x = sin^-1(3x – 4x³), x Є [-1/2, 1/2].

Prove that 3sin^-1 x = sin^-1(3x – 4x³), x Є [-1/2, 1/2]

Prove that 3 cos^-1 x = cos^-1(4x³ – 3x), x Є [1/2, 1].

Prove that 3 cos^-1 x = cos^-1(4x³ – 3x), x Є [1/2, 1]

Prove that: tan^-1 (2/11) + tan^-1 (7/24) = tan^-1 (1/2).

Prove that: tan^-1  + tan^-1  = tan^-1

Prove that: 2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17).

Prove that:

Write the function tan^-1{√(1 + x²) - 1}/x, x ≠ 0, in the simplest form.

Write the function , in the simplest form.

Write the function tan^-1{1/√(1 + x²)}, |x| > 1, in the simplest form.

Write the function  , in the simplest form.

Write the function tan^-1[√{(1 – cos x)/(1 + cos x)}], x < π in the simplest form.

Write the function   in the simplest form.

Write the function , 0 < x < π in the simplest form.

Write the function tan^-1[(cos x –sin x)/(cos x + sin x)], 0 < x < π in the simplest form.

Write the function tan^-1  , |x| < a in the simplest form.

Write the function tan^-1[x/√(a² – x²)], |x| < a in the simplest form.

Write the function in  the simplest form.      

Write the function in tan^-1[(3a²x – x³)/(a³ – 3ax²)], a > 0, -a/√3 ≤ x ≤ a/√3 the simplest form.      

Find the value if

Find the value if tan^-1[2 cos(2 sin^-1 1/2)].

Find the value of cot(tan^-1 a + cot^-1 a)

Find the value of cot(tan^-1 a + cot^-1 a).

Find the value of    and

Find the value of tan [sin^-1{2x/(1 + x²)} + cos^-1{(1 – y²)/(1 + y²)}]/2, |x| < 0, y > 0 and xy < 1.

If sin(sin^-1 1/5 + cos^-1 x) = 1, then find the value of x.

If sin(sin^-1  + cos^-1 x) = 1, then find the value of x.

If , then find the value of x.

If tan^-1 {(x - 1)/(x - 2)} + tan^-1 {(x + 1)/(x + 2)} = π/4, then find the value of x.

Find the value of sin^-1  

Find the value of sin^-1(sin 2π/3).

Find the value of  

Find the value of tan^-1(tan 3π/4).

Find the value of tan(sin^-1  + cot^-1 )

Find the value of tan(sin^-1 3/5 + cot^-1 3/2).

cos^-1(cos ) is equal to

(A) 7π/6                            

(B) 5π/6                        

(C) π/3                              

(D) π/6

cos^-1(cos 7π/6) is equal to

(A) 7π/6                             (B) 5π/6                         (C) π/3                               (D) π/6

Find the value of    

Find the value of sin(π/3- sin^-1 (-1/2)) .

tan^-1 √3 - cot^-1 (-√3) is equal to

(A) π                           (B) - π/2                        (C) 0                                    (D) 2√3

Find the value of cos^-1(cos ).

Find the value of cos^-1(cos 13π/6).

Find the value of tan^-1(tan ).

Find the value of tan^-1(tan 7π/6).

Prove that 2sin^-1 3/5 = tan^-1 24/7.

Prove that

Prove that sin^-1 8/17 + sin^-1 3/5 = tan^-1 77/36.

Prove that sin^-1  + sin^-1  = tan^-1

Prove that cos^-1 4/5 + cos^-1 12/13 = cos^-1 33/65.

Prove that cos^-1  + cos^-1  = cos^-1

Prove that cos^-1 12/13 + sin^-1 3/5 = sin^-1 56/65.

Prove that cos^-1  + sin^-1  = sin^-1

Prove that tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5.

Prove that  

Prove that tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/3 + tan^-1 1/8 = π/4.

Prove that

Prove that tan^-1 √x = (1/2) * cos^-1 {(1 - x)/(1 + x)}, x Є [0, 1].

Prove that  =   , x Є [0, 1]

Prove that

Prove that cot^-1 [{√(1 + sin x) + √(1 - sin x)}/{ √(1 + sin x) - √(1 - sin x)}] = x/2, x Є (0, π/4).

Prove that tan^-1 [{√(1 + x) - √(1 - x)}/{√(1 + x) + √(1 - x)}] = π/4 - (1/2)cos^-1 x, -1/√2 ≤ x ≤ 1.

Prove that 

9π/8 – (9/4)sin^-1 1/3 = (9/4)sin^-1 2√2/3

Solve for x: 2tan^-1(cos x) = tan^-1(2cosec x)

Solve for x: 2tan^-1(cos x) = tan^-1(2cosec x)

Solve for   

Solve for x: tan^-1 {(1 - x)/(1 + x)} = (1/2)tan^-1 x, x > 0.

sin(tan^-1 x), |x| < 1 is equal to

(A) x/√(1 – x²)                  (B) 1/√(1 – x²)                     

(C) 1/√(1 + x²)                  (D) x/√(1 + x²)

sin(tan^-1 x), |x| < 1 is equal to

(A)            

(B)      

(C)         

(D)

sin^-1(1 – x) - 2sin^-1 x = π/2, then x is equal to

(A) 0, 1/2                           

(B) 1, 1/2                              

(C) 0                            

(D) 1/2

sin^-1(1 – x) - 2sin^-1 x = π/2, then x is equal to

(A) 0, 1/2                            (B) 1, 1/2                               (C) 0                             (D) 1/2

  is equal to

(A) π/2                              

(B) π/3                        

(C) π/4                           

(D) -3π/4

tan^-1  x/y - tan^-1{(x – y)/(x + y)} is equal to

(A) π/2                               (B) π/3                         (C) π/4                            (D) -3π/4