if `sin^-1((2p)/(1+p^2))-cos^-1((1-q^2)/(1+q^2))=tan^((2x)/(1-x^2))` prove that `x=(p-q)/(1+pq)` where `p,qepsilon(0,1)`

if quad sin^(-1)((2p)/(1+p^(2)))-cos^(-1)((1-q^(2))/(1+q^(2)))=tan^((2 pi)/(1-z^(2))) prove that x=(p-q)/(1+pq) where p,q varepsilon(0,1)

If Sin^(-1)(2p)/(1+p^(2)) - Cos^(-1)((1-q^(2))/(1+q^(2))) = Tan^(-1) (2x)/(1-x^(2)) , then prove that x = (p-q)/(1+pq)

int((p+q tan^(-1)x))/(1+x^(2))dx

Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1) sqrt((p-x)/(p-q))="cot"^(-1) sqrt((p-x)/(x-q))

tan ^(-1)""(1)/(p+q)+tan ^(-1)""(q)/(p^(2)+pq+1)=cot^(-1)p

If int (2tan x+3)/(sin^(2)x+2cos^(2)x)dx =1_(n)(1+sec^(2)x)+ p tan^(-1)((tanx)/(q))+c ,then pq is

tan ^ (- 1) ((1) / (p + q)) + tan ^ (- 1) ((a) / (p ^ (2) + q + 1)) = cos ^ (- 1) p