" 18Promethat: "(sin2x)/(1+cos2x)=tan x

Prove that (sin x)/(1+cos x)=tan((x)/(2))

Prove that (sin4x+sin2x)/(cos4x+cos2x)=tan3x

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

Prove that: (1+sin2x-cos2x)/(1+sin2x+cos2x)=tanx

int(sin^(2)x)/(1+cos2x)dx=k (tan x-x)+c then k is equal to

Prove that (1+ sin 2x - cos 2x)/(1+ sin 2x + cos 2x) =tan x

Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos [tan^(-1) (cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

Prove that (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x) = 2 tan x

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

Prove that: (i) (1+"sin" 2theta-cos 2theta)/(1+"sin" 2theta+cos 2theta)="tan" theta . (ii) 2 tan 2x=(cos x+"sin" x)/(cos x-"sin" x)-(cos x-"sin" x)/(cos x+"sin" x) .