Prove that: `tan^-1 ((a_1x-y)/(x+a_1y))+tan^-1 ((a_2-a_1)/(1+a_1a_1))+tan^-1 ((a_3-a_2)/(1+a_3a_2))+…+tan^-1, ((a_n-a_(n-1)/(1+a_na_(n-1))+tan^-1 (1/a_n)=tan^-1, x/y`

If 0

If c_i >0 for i=1,\ 2,\ ,\ n , prove that tan^(-1)((c_1x-y)/(c_1y+x))+tan^(-1)((c_2-c_1)/(1+c_2c_1))+tan^(-1)((c_3-c_2)/(1+c_3c_2))+\ dot+tan^(-1)(1/(c_n))=tan^(-1)(x/y)

If c_(j)>0 for i=1,2,......,n prove that tan^(-1)((c_(1)x-y)/(c_(1)y+x))+tan^(-1)((c_(2)-c_(1))/(1+c_(2)c_(1)))+tan^(-1)((c_(3)-c_(2))/(1+c_(3)c_(2)))+......+(tan^(-1)1)/(c_(n))=tan^(-1)((x)/(y))

Prove that tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)((2x)/(2-x^2))

Prove that tan ^ (- 1) ((1) / (3)) + tan ^ (- 1) ((1) / (7)) + tan ^ (- 1) ((1) / (13)) + ......... + tan ^ (- 1) ((1) / (n ^ (2) + n + 1)) +

Prove that tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3)) .

Prove that tan(2tan^(-1)x)=2tan(tan^(-1)x+tan^(-1)x^(3))

Prove that: int tan^(n)xdx=(1)/(n-1)tan^(n-1)x-int tan^(n-2)xdx

Prove that: int tan^(n)xdx=(1)/(n-1)tan^(n-1)x-int tan^(n-2)xdx