[" If: "a=tan x,b=tan y,c=sqrt(1+a^(2)),d=sqrt(1+b^(2))," then: "],[cd sin(x+y)=]

If y=sqrt((a-x)(x-b))-(a-b)tan^(-1)((sqrt(a-x))/(sqrt(x-b))) then (dy)/(dx)=

If x=sin(2tan^(-1)2sqrt3)and y=sin((1)/(2)tan^(-1).(12)/(5)) , then

"If "y=(2)/(sqrt(a^(2)-b^(2))){tan^(-1)(sqrt((a-b)/(a+b))tan""(x)/(2))}," then show that "(d^(2)y)/(dx^(2))=(b sin x)/((a+b cos x)^(2)).

If tan A= 1/(sqrt(x(x^2+x+1))), tan B = sqrtx/(sqrt (x^2+ x+ 1)) and tan C = sqrt(x^(-3)+x^(-2)+x^(-1)) , prove that A+B=C.

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

If tan^(-1)x+cos^(-1)((y)/(sqrt(1+y^(2))))=sin^(-1)((3)/(sqrt(10))) , then

tan ^(-1)x-tan ^(-1)y=sin ^(-1) ""(x-y)/(sqrt((1+x^(2))(1+y^(2)))