Statement 1 - If f ( x ) = sin − 1 x + cosec − 1 x + cos − 1 x + sec − 1 x + tan − 1 x , then f ( x ) can take every value in the interval ( 2 π , 2 3 π ) . Statement 2 - f ( x ) = π + tan − 1 x a

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Statement 1 - If f ( x ) = sin − 1 x + cosec − 1 x + cos − 1 x + sec − 1 x + tan − 1 x , then f ( x ) can take every value in the interval ( 2 π ​ , 2 3 π ​ ) . Statement 2 - f ( x ) = π + tan − 1 x and − 2 π ​ < tan − 1 x < 2 π ​ ∀ x .

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f is defined only for x = ± 1 (domain of cosec − 1 and sec − 1 meets [ − 1 , 1 ] ), so it takes just two values, 4 5 π ​ and 4 3 π ​ . Statement 1 is false. There f ( x ) = π + tan − 1 x and tan − 1 x ∈ ( − 2 π ​ , 2 π ​ ) , so Statement 2 is true.

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

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