Complete solution set of `tan^2(sin^(-1)x)>1` is (a)`(-1,-1/(sqrt(2)))uu(1/(sqrt(2)),1)` (b) `(-1/(sqrt(2)),1/(sqrt(2)))~{0}` (c)`(-1,1)~{0}` (d) none of these

A(1/(sqrt(2)),1/(sqrt(2))) is a point on the circle x^2+y^2=1 and B is another point on the circle such that arc length A B=pi/2 units. Then, the coordinates of B can be (a) (1/(sqrt(2)),-1/sqrt(2)) (b) (-1/(sqrt(2)),1/sqrt(2)) (c) (-1/(sqrt(2)),-1/(sqrt(2))) (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

The solution of the inequality (log)_(1//2) sin^(-1)x >(log)_(1//2)cos^(-1)x is (a) x in [0,(1)/(sqrt(2))] (b) x in [1/(sqrt(2)),1] (c) x in (0,(1)/(sqrt(2))) (d) none of these

The value of lim_(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-1)x))) is (a) -1/(sqrt(2)) (b) 1/(sqrt(2)) (c) sqrt(2) (d) -sqrt(2)

If |cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n (a) x in [-1/3,1/(sqrt(3))] (b) x in [-1/(sqrt(3)),1/(sqrt(3))] x in [0,1/(sqrt(3))] (d) none of these

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

int_(0)^((1)/(2))(xsin^(-1)x)/(sqrt(1-x^(2)))dx=(1)/(2)(1-(pi)/(2sqrt(3)))

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

The value of sin^(-1)("cot"(sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)((sqrt(12))/4)+sec^(-1)sqrt(2)))i s (a) 0 (b) pi/2 (c) pi/3 (d) none of these

A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2) and f(x) is an increasing function. Then g(x) is increasing in the interval. (a) (-1,1) (b) (-sqrt(2/3),0)uu(sqrt(2/3),oo) (c) (-sqrt(2/3),sqrt(2/3)) (d) none of these