`tan^(-1)a+tan^(-1)b=(cos^(-1) )(1-ab)/(sqrt((1+a^2)(1+b^2)))`

Prove that, tan^(-1)a+tan^(-1)b+tan^(-1)((1-a-b-ab)/(1+a+b-ab))=(pi)/(4) .

int(1)/(a^(2)-b^(2)cos^(2)x)dx(a>b)=(1)/(a sqrt(a^(2)-b^(2)))tan^(-1)[(a tan x)/(sqrt(a^(2)-b^(2)))]+c

The expression (1)/(sqrt(2)){(sin tan^(-1)cos tan^(-1)t)/(cos tan^(-1)sin cot^(-1)sqrt(2)t)}*{sqrt((1+2t^(2))/(2+t^(2)))}

Prove that: tan[(pi)/(4)+(1)/(2) tan^(-1)((a)/(b))]+tan[(pi)/(4)-(1)/(2)tan^(-1)((a)/(b))]=(2sqrt(a^(2)+b^(2)))/(b)

a=sin^(-1)(-(sqrt(2))/(2))+cos^(-1)(-(1)/(2)) and b=tan^(-1)(-sqrt(3))-cot^(-1)(-(1)/(sqrt(3))) ,then

Prove that : cos ^(-1) ((1- a^(2))/(1+a)) + cos ^(-1)((1-b^(2))/(1+b^(2))) = 2 tan ^(-1) .(a+b)/(1-ab)

sin^(-1) ""(2a)/(1+a^(2))-cos^(-1) ""(1-b^(2))/(1+b^(2))=2tan ^(-1) ""(a-b)/(1+ab)

Prove that : cos ^(-1) ((1- a^(2))/(1+a^2)) + cos ^(-1)((1-b^(2))/(1+b^(2))) = 2 tan ^(-1) .((a+b)/(1-ab))

If ab lt 1 and cos ^(-1) ((1 - a ^(2))/( 1 + a ^(2))) + cos ^(-1) ((1 - b ^(2))/( 1 + b ^(2)))= 2 tan ^(-1)x, then x is equal to

sin^(-1)(2(a)/(1)+a^(2))+(cos^(-1)(1-b^(2)))/(1+b^(2))=tan^(-1)(2(a)/(1)-x^(2)) the provet widehat x=(a-b)/(1+ab)