10.If `1/2+1/x`=2, then x=

If cos theta =1/2 (x+1/x ) , then 1/2(x^(2) +1/(x^(2))) is equal to :

If tan^(- 1)((2x)/(x^2-1))+cos^(- 1){(x^2-1)/(x^2+1)}=(2pi)/3 then x=

If x_(1) = 2 tan^(-1) ((1 + x)/(1 -x)), x_(2) = sin^(-1) ((1 - x^(2))/(1 + x^(2))), " where " x in (0, 1) , then 2( x_(1) + x_(2) ) is equal to

If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

If f(x)={((x-2)2^(-(1/(|x-2|)+1/(x-2))),x!=2),(0,x=2):} then f(x) at x=2 is

If sin^(-1)(2x)/(1+x^2)=tan^(-1)(2x)/(1-x^2) , then find the value of xdot

If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree- a. 2 b. \ 3 c. \ 0 d. 1

If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) is equal to (a) 1/(2(1+x^2)),x in R (b) 1/(2(1+x^2)),x >0 (c) (-1)/(2(1+x^2)),x<0 (d) 1/(2(1+x^2)),x<0

Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , with respect to x , if x in (0,\ 1) .

Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , with respect to x , if x in (1,\ oo)