The inverse of a function f:A #x2192;B exists if f is one one onto i.e., y=f( x ) #x21D2; f #x2212;1 ( y )=x . The gi ...

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Domain and Range of Basic Inverse Trigonometric Functions

4. tan 34. ta...

Question

4. tan 3)4. tan-V3)

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Solution

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 tan −1 ( − 3 ) .

Let,

tan -1 ( − 3 )=y

tany=− 3 =−tan π 3 =tan( − π 3 )

Since, the range of the principle value branch of tan -1 is ( − π 2 , π 2 ) .

− π 3 ∈( − π 2 , π 2 )

Thus, the principle value of tan −1 ( 3 ) is ( − π 3 ) .

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