The expression `(tan^4x+2tan^2x+1)cos^2x ,w h e nx=pi/(12),` can be equal to (a)`4(2-sqrt(3))` (b) `4(sqrt(2)+1)` (c)`16cos^2pi/(12)` (d) `16sin^2pi/(12)`

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)

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

2tan^(-1)(-2) is equal to (a) -cos t^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (c) -pi/2+tan^(-1)(-3/4) (d) -picot^(-1)(-3/4)

If cos^-1((x^2 -1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3 , then x equal to (A) sqrt(3) (B) 2+sqrt(3) (C) 2-sqrt(3) (D) -sqrt(3)

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 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 tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

The numerical value of tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)+8tan((8pi)/3) is equal to (A) -5sqrt(3) (B) -5/(sqrt3) (C) 5sqrt(3) (D) 5/(sqrt3)

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x