" प्रश्न "21.tan^(2)(2x-3)

Prove that tan^(-1) ((3x-x^(3))/(1-3x^(2)))=tan^(-1)x +"tan"^(-1)(2x)/(1-x^(2)), |x| lt (1)/(sqrt(3)) .

Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(3))/(1-3x^(2)) , |x| lt 1/(sqrt(3))

Let |{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3x), (tan^(-1)3x, tan^(-1)x, tan^(-1)2x), (tan^(-1)2x, tan^(-1)3x, tan^(-1)x):}|=0 , then the number of values of x satisfying the equation is

(d) / (dx) [((tan ^ (2) 2x-tan ^ (2) x) / (1-tan ^ (2) 2x tan ^ (2) x)) cot3x] =

Prove that : 2 tan^(-1) (1/3) +tan^(-1) (1/6) = tan^(-1) (22/21)

Solve : tan^(2)x*tan^(2)3x*tan4x=tan^(2)x-tan^(2)3x+tan4x

lim_(x rarr tan^(-1)) (tan^(2)x - 2tanx -3)/(tan^(2)x - 4tan x +3 ) =

Show that tan 3 x=(3 tan x-tan ^(3) x)/(1-3 tan ^(2) x)

lim_ (x rarr tan ^ (- 1) 3) ([tan ^ (2) x] -2 [tan x] -3) / ([tan ^ (2) x] -4 [tan x] +3) where [*]