Which of the following is the solution set of the equation `2cos^(-1)x=cot^(-1)((2x^2-1)/(2xsqrt(1-x^2)))?`(0, 1) `(b)`(-1, 1) -{0}`(-1,0)`(d) `(-oo,-1)uu[1,oo]`A. `(0,1)`B. `(-1, 1) - {0}`C. `(-1, 0)`D. `[-1, 1]`

Which of the following is the solution set of the equation `2cos^(-1)x

1.	Which of the following is the solution set of the equation `2cos^(-1)x=cot^(-1)((2x^2-1)/(2xsqrt(1-x^2)))?`(0, 1) `(b)`(-1, 1) -{0}`(-1,0)`(d) `(-oo,-1)uu[1,oo]`A. `(0,1)`B. `(-1, 1) - {0}`C. `(-1, 0)`D. `[-1, 1]`
Answer» Correct Answer - A `2 cos^(-1) x = cot^(-1) ((2x^(2) -1)/(2x sqrt(1 -x^(2))))` Put `x = cos theta : L.H.S. = 2 theta, 0 le theta le pi` and `-1 le x le 1`...(i) `R.H.S. = cot^(-1) ((cos 2 theta)/(2 cos theta\|sin theta\|)) = cot^(-1) (cot 2 theta) = 2 theta` if `0 lt 2 theta le pi`...(ii) From Eqs. (i) and (ii) , we get `0 lt theta lt pi//2`. Thus, `x in (0, 1)`

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