" (i) "sin^(-1)(2 alpha)/(1+alpha^(2))+sin^(-1)(2 beta)/(1+beta^(2))=2tan^(-1)x,| alpha|<=|1,| beta|<=|1

Solve : sin^(-1)((2alpha)/(1+alpha^2)) + sin^(-1)( (2beta)/(1+beta^2)) =2 tan^(-1) x, |alpha|le1, |beta|le1

Solve : sin^(-1)((2alpha)/(1+alpha^2)) + sin^(-1)( (2beta)/(1+beta^2)) =2 tan^(-1) x, |alpha|le1, |beta|le1

Solve for x, "sin"^(-1)((2alpha)/(1+alpha^(2)))+"sin"^(-1)((2beta)/(1+beta^(2)))=2"tan"^(-1)x .

x: (sin ^ (- 1) (2 alpha)) / (1 + a ^ (2)) + (sin ^ (- 1) (2 beta)) / (1 + beta ^ (2)) = 2tan ^ (-1) x

If tan^(-1)(alpha+i beta)=a+ib, then a= 1). (1)/(2)tan^(-1)((2 alpha)/(1-alpha^(2)-beta^(2))) 2) . (1)/(2)tan^(-1)((2 alpha)/(1+alpha^(2)+beta^(2))) 3). tan^(-1)((2 alpha)/(1-alpha^(2)-beta^(2))) 4). (1)/(2)tan^(-1)((2 beta)/(1+alpha^(2)+beta^(2)))

Show taht 2tan ^ (- 1) (tan ((alpha) / (2)) tan ((pi) / (4) - (beta) / (2))) = tan ^ (- 1) ((sin alpha cos beta) / (cos alpha + sin beta))

tan alpha=(1+2^(-x))^(-1),tan beta=(1+2^(x+1))^(-1)alpha+beta

Prove that 2tan^(-1)[tan((alpha)/(2)) tan((pi)/(4)-(beta)/(2))]=tan^(-1)((sin alpha cos beta)/(cos alpha+sin beta))

Prove that: (alpha^(3))/(2)csc^(2)((1)/(2)tan^(-1)(alpha)/(beta))+(beta^(2))/(2)sec^(2)((1)/(2)tan^(-1)(beta)/(alpha))=(alpha+beta)(a^(2)+beta^(2))