Match List I to List II. List I: (A) Absolute difference between greatest and least values of 2 ( sin 2 x − cos 2 x ) ; (B) Absolute difference between greatest and least values of x 2 − 4 x + 3 , x

Question

Match List I to List II. List I: (A) Absolute difference between greatest and least values of $2 (sin 2 x - cos 2 x)$ ; (B) Absolute difference between greatest and least values of $x^{2} - 4 x + 3, x \in [1, 3]$ ; (C) Greatest value of $tan^{- 1} ((1 - x) / (1 + x))$ , $x \in [0, 1]$ ; (D) Absolute difference between greatest and least values of $cos^{- 1} (x^{2}), x \in [- 1/ 2, 1/ 2]$ . List II: $(P) π /4$ ; (Q) $π /6; (R) 4; (S) 1; (T) π /3$ .

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Answer:

A

Solution:

A: amplitude is 2, hence range [-2,2] and difference 4. B: values at 1,2,3 are 0,-1,0; difference 1. C: $tan^{- 1} ((1 - x) / (1 + x)) = π /4 - tan^{- 1} x$ , largest $π /4$ at $x = 0$ . D: $cos^{- 1} (x^{2})$ ranges from $π /3$ to $π /2$ , difference $π /6$ .

TestHub · Accepted Answer

A: amplitude is 2, hence range [-2,2] and difference 4. B: values at 1,2,3 are 0,-1,0; difference 1. C: tan − 1 (( 1 − x ) / ( 1 + x )) = π /4 − tan − 1 x , largest π /4 at x = 0 . D: cos − 1 ( x 2 ) ranges from π /3 to π /2 , difference π /6 .

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

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