tan^(-1)(21)/(sqrt(a^(2)-2^(2)))

tan^(-1)[x/sqrt(a^(2)-x^(2))]=

d//dx[tan^(-1)((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))^(1//2)]

The value of tan^(-1)((1)/(sqrt(2)))-tan^(-1)((sqrt(5-2sqrt(6)))/(1+sqrt(6))) is equal to

(1)/(sqrt(21+4x-x^(2)))

tan^(-1)((sqrt(2)+1)/(sqrt(2)-1)) - tan^(-1)(sqrt(2)/2) =

quad Ifalpha=2tan^(-1)(sqrt(3-2sqrt(2)))+sin^(-1)((1)/(sqrt(6)-sqrt(2))),beta=cot^(-1)(sqrt(3)-2)+(1)/(8)sec^(-1)(-2) and gamma=tan^(-1)((1)/(sqrt(2)))+cos^(-1)((1)/(sqrt(3))), then

A: int (1)/(3+2 cos x)dx=(2)/(sqrt(5))"Tan"^(-1)((1)/(sqrt(5))"tan" (x)/(2))+c R: If a gt b then int (dx)/(a+b cosx)=(2)/(sqrt(a^(2)-b^(2)))Tan^(-1)[(sqrt(a-b))/(a+b)"tan"(x)/(2)]+c

tan(2tan^(-1)((sqrt(5)-1)/(2)))=

(d )/(dx ) { (2)/( sqrt(a ^(2) - b ^(2))) Tan ^(-1) (( sqrt (a -b ))/( a + b) tan (x )/(2 )) }=

3(tan^(-1)1)/(2+sqrt(3))-(tan^(-1)1)/(2)=(tan^(-1)1)/(3)