9, cos' (-
The inverse of a function f : A → B exists if f is one-one onto i.e.,
y = f ( x ) ⇒ f − 1 ( y ) = x .
The given inverse trigonometry function is cos − 1 ( − 1 2 ) .
Let,
cos -1 ( − 1 2 ) =y
cos y = − 1 2 = − cos ( π 4 ) = cos ( π − π 4 ) = cos ( 3 π 4 )
Since, the range of the principle value branch of cosec -1 is [ 0 , π ] .
3 π 4 ∈ [ 0 , π ]
Thus, the principle value of cos -1 ( − 1 2 ) is ( 3 π 4 ) .
The inverse of a function
The given inverse trigonometry function is
Let,
Since, the range of the principle value branch of
Thus, the principle value of
