i log((x-i)/(x+i))=pi-2tan^(-1)x

For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=1/(e^(pi))(pi-4tan^(-1)x)

For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=1/(e^(pi))(pi-4tan^(-1)x)

Simplify: i log((x-i)/(x+i))

int _ (-2)^(1) (tan^(-1) ((x)/(x^(2) +1))+tan^(-1) ((x^(2) +1)/( x))) dx is (i) (pi)/(2) (ii)-(pi)/(2) (iii) pi (iv) -pi

Prove that log ((sin(x+iy))/(sin(x-iy))) = 2i tan^-1 ( cot x tan hy).

sin^(2) x+2sin x cos x-3cos^(2) x = 0 if (i) tan x = 3 (ii) tan x = -1 (iii) x = n pi+(pi)/(4) , n in I (iv) x = n pi+tan^(-1) (3), n in I

If I_(1)=lim_(xto oo)(tan^(-1)pi x- tan^(-1)x)cosx and I_(2)=lim_(xto0)(tan^(-1)pi x-tan^(-1)x)cosx then (I_(1),I_(2)) is

If I_(1)=lim_(xto 0)(tan^(-1)pi x- tan^(-1)x)cosx and I_(2)=lim_(xto0)(tan^(-1)pi x-tan^(-1)x)sinx then (I_(1),I_(2)) is

If I_(1)=lim_(xto oo)(tan^(-1)pi x- tan^(-1)x)cosx and I_(2)=lim_(xto0)(tan^(-1)pi x-tan^(-1)x)cosx then (I_(1),I_(2)) is