-1
By Team Aakash Byju's | 13th November 2022
[0, π] - { }
(0, π)
(π, )
(0, π) - { }
π
2
π
2
π
4
Detailed Explanation
-1
π
2
The principal value is the value of the inverse trigonometric function lying in the range of its principal branch.
The smallest value of θ, either positive or negative .
Function
Domain
x
Range
y
sin x
cos x
tan x
cosec x
sec x
cot x
-1
-1
-1
-1
-1
-1
[-1,1]
[-1,1]
R=(-∞,∞)
R-(-1,1)
R-(-1,1)
R
[ ]
π
2
-
,
π
2
[0 , π ]
( )
-
π
2
π
2
,
π
2
-
π
2
,
[ ]
,
y ≠ 0
y ≠
[ ]
,
-
π
2
π
2
π
2
,
(0 , )
π
We know that the domain of the function y = sec (x) is x ≤ -1 or x ≥ 1.
-1
y = sec x
-1
So, the valid range for sec(y) = x is between 0 and π.
sec (-1) = π and sec (1) = 0
Range for sec(y) = x is [0, π]
-1
-1
y = sec x
-1
y = sec x
π
2
π
2
cos( ) = 0
π
2
sec( ) =
π
2
cos( )
π
2
1
=
1
0
sec( ) =
π
2
undefined
But, sec( ) is undefined as cos( ) = 0
-1
y = sec x
Therefore, the principal value branch of sec (x) will be
-1
[0, π] -
{ }
π
2
-1