If `2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n` tan A is equal `1//sqrt(2)` (b) `1/2` (c) `1/2sqrt(2)` (d) `-1/(sqrt(2))`

If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) (b) 1/2 (c) 1 (d) sqrt(2)

If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) (b) 1/2 (c) 1 (d) sqrt(2)

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

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)

Ifint_(-pi/4)^((3pi)/4)((e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx))=kint_(-pi/2)^(pi/2)secx dx ,t h e nt h ev a l u eofki s 1/2 (b) 1/(sqrt(2)) (c) 1/(2sqrt(2)) (d) -1/(sqrt(2))

If sinx+cos e cx=2, then sin^n x+cos e c^n x is equal to 2 (b) 2^n (c) 2^(n-1) (d) 2^(n-2)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals. (a) (x+sqrt(x^2-4))/2 (b) x/(1+x^2) (c) (x-sqrt(x^2-4))/2 (d) 1+sqrt(x^2-4)

sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3) is equal to (a)5 (b) 13 (c) 15 (d) 6