Mathematics > Inverse Trigonometric Functions

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Functions

Domain

Range

(Principal Value Ranges)

[-1, 1]

[-1, 1]

R- (-1, 1)

R- (-1, 1)

R

R

   

   

  • The value of inverse trigonometric functions which lies in its principal value branch is called the principal value of that inverse trigonometric functions.
  • y = sin–1 x x = sin y
  • x = sin y y = sin–1 x
  • sin (sin–1 x) = x
  • sin–1(sin x) = x
  • cos–1 (–x) = π – cos–1 x
  • cot–1 (–x) = π – cot–1 x
  • sec–1 (–x) = π – sec–1 x
  • sin–1(–x) = – sin–1 x
  • tan–1 (–x) = – tan–1 x
  • tan–1 x + cot–1 x =
  • cosec–1 (–x) = – cosec–1 x
  • sin–1 x + cos–1 x =
  • cosec–1 x + sec–1 x =
  •  

 

Examples

Question

Find the principal value of

Solution

 = y

We know that the range of the principal value branch of  is, and

Hence the value of is

 

Question

Show that

Solution

   

Let  Then

                         =

                         =

                        

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