" 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)) .

(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

show that tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/sqrt3

tan^(-1)x+(tan^(-1)(2x))/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3))

show that tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/sqrt3

If sin A=(2)/(5), find the value of 21+21tan^(2)A

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