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

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

Solve the equations. sin(tan^(-1)x),|x|<1 (A) x/(sqrt(1-x^2)) (B) 1/(sqrt(1-x^2)) (C) 1/(sqrt(1+x^2)) (D) x/(sqrt(1+x^2))

The complete solution set of the equation sin^(-1) sqrt((1+x)/(2))-sqrt(2-x)=cot^(-1)(tan sqrt(2-x))-sin^(-1) sqrt((1-x)/(2)) is :

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

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

The value of ("lim")_(xvec2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (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

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

Differential coefficient of sec(tan^(-1)x) is (a) x/(1+x^2) (b) xsqrt(1+x^2) (c) 1/(sqrt(1+x^2)) (d) x/(sqrt(1+x^2))