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

prove that 2tan^(-1)(sqrt((a-b)/(a+b))tan((theta)/(2)))=cos^(-1)((a cos theta+b)/(a+b cos theta))

If a,b,c>0 and s=(a+b+c)/(2), prove thattan^(-1)sqrt((2as)/(bc))+tan^(-1)sqrt((2bs)/(ca))+tan^(-1)sqrt((2cs)/(ab))=pi

Prove that: tan^(-1){(pi)/(4)+(1)/(2)(cos^(-1)a)/(b)}+tan{(pi)/(4)-(1)/(2)(cos^(-1)a)/(b)}=(2b)/(a)

Prove that tan((pi)/(4)+(1)/(2)cos^(-1)((a)/(b)))+tan((pi)/(4)-(1)/(2)cos^(-1)((a)/(b)))=(2b)/(a)

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

Prove the following: tan[(pi)/(4)+(1)/(2)cos^(-1)((a)/(b))]+tan[(pi)/(4)-(1)/(2)cos^(-1)((a)/(b))]=(2b)/(a)

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)

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) = pi

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

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