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restricted to any of the intervals etc is bijective 2 2 2 2 2 2...

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Algebra

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restricted to any of the intervals etc is bijective 2 2 2 2 2 2 and its range is R Thus tan can be defined as a function whose domain is R and range could be any of the intervals intervals give different branches of the function tan The branch with range is called the principal value branch of the function tan We thus have tan R The graphs of the function y tan x and y tan x are given Y y tan x intervals T 2 3 3 17 19 4 2 2 2 2 2 2 T T T 3 2 NCER X Rationalised 2023 24 and so on These 2 1 TC T Fig 2 5 i ii 2 3T 2 T 2 O 12 TC 2 2 Y y tan x republished Fig 2 5 i Fig 2 5 ii We know that domain of the cot function cotangent function is the set x x R and x n n Z and range is R It means that cotangent function is not defined for integral multiples of If we restrict the domain of cotangent function to 0 then it is bijective with and its range as R In fact cotangent function restricted to any of the intervals 0 0 2 etc is bijective and its range is R Thus cot can be defined as a function whose domain is the R and range as any of the X INVERSE TRIGONOMETRIC FUNCTIONS 25 2 ete These intervals give different branches of the

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