" 10."tan^(-1)((sin2x)/(1+cos2x))

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Evaluate the following integrals: int tan^(-1)((sin2x)/(1+cos2x))dx

Evaluate: (i) int tan^(-1)((sin2x)/(1+cos2x))dx( ii) int cos^(-1)(sin x)dx

Prove that , tan^(-1)((2 sin 2x)/(1+2 cos 2x))-(1)/(2)sin^(-1)((3 sin 2x)/(5+4 cos 2x))=x .

int tan^(-1) ((sin2x)/(1+cos 2x))dx

Prove that, tan^(-1)((3 sin 2x)/(5+3 cos 2x))+tan^(-1)((1)/(4) tan x)=x .

(sin2x)/(1+cos2x)=tan x

Evaluate: (i) int cot^(-1)((sin2x)/(1-cos2x))dx (ii) int sin^(-1)((2tan x)/(1+tan^(2)x))dx

Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2tanx)/(1+tan^2x))\ dx

Prove that tan^-1 ((3sin2x)/(5+3 cos2x)) + tan^-1(1/4 tanx = x .