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y cosec x 07 201 restrict the domain of secant function to 0 x 0...

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Calculus

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y cosec x 07 201 restrict the domain of secant function to 0 x 0 y see x 0 1 the domain of y secx is the set R x x 2n 1 COS X n Z and range is the set R 1 1 It means that sec secant function assumes all real values except 1 1 and is not defined for odd multiples of 3 If we Y y cosec x Rationalised 2023 24 Fig 2 3 ii then it is one one and onto with its range as the set R 1 1 Actually secant function restricted to any of the 3x intervals 1 0 0 n 2n etc is bijective and its range 3x is R 1 1 Thus sec can be defined as a function whose domain is R 1 1 and range could be any of the intervals 7 0 0 n 2n etc Corresponding to each of these intervals we get different branches of the function sec The branch with range 0 is called the principal value branch of the function sec We thus have R R 1 1 0 x 1 A 2 INVERSE TRIGONOMETRIC FUNCTIONS 23 see 161 The graphs of the functions y sec x and y sec x are given in Fig 2 4 1 ii CERT reptableted y sec x

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