Which of the following quantities is/are positive ?A. `cos (tan^(-1) (tan 4))`B. `sin(cot^(-1)(cot 4))`C. `tan (cos^(-1) (cos 5))`D. `cot(sin^(-1) (sin 4))`

Which of the following quantities is/are positive ?A. `cos (tan^(-1) (

1.	Which of the following quantities is/are positive ?A. `cos (tan^(-1) (tan 4))`B. `sin(cot^(-1)(cot 4))`C. `tan (cos^(-1) (cos 5))`D. `cot(sin^(-1) (sin 4))`
Answer» Correct Answer - A::B::C (1) `cos (tan^(-1) (tan (4 - pi)))` `= cos(4 - pi) = cos (pi -4) = - cos 4 gt 0` (2) `sin(cot^(-1) (cot(4 - pi)))` `= sin(4 - pi) = - sin 4 gt 0 ("as " sin 4 lt 0)` (3) `tan (cos^(-1) (cos (2 pi - 5)))` `= tan (2pi - 5) = -tan 5 gt 0 ("as " tan 5 lt 0)` (4) `cot(sin^(-1) (sin (pi -4)) = cot (pi -4) = - cot 4 lt 0`

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