3tan^(2)x+cos^(1)x=x

The integral int(sin^(2)x cos^(2)x)/((sin^(5)x+cos^(3)x sin^(2)x+sin^(3)x cos^(2)x+cos^(5)x)^(2))dx is equal to (1) (1)/(3(1+tan^(3)x))+C(2)(-1)/(3(1+tan^(3)x))+C(3)(1)/(1+cot^(3)x)+C(4)(-1)/(1+cot^(3)x)+C

If cos^(2) x + cos^(4) x =1 then tan^(2) x + tan^(4) x=

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

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

If cos^(2)x+cos^(4)x=1 , then find the value of tan^(2)x+tan^(4)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))

If cos^(2)x+cos^(4)x=1 then tan^(2)x+tan^(4)x=1)12)03)-14)2

range of the function f(x)=cos^(-1)x+2sin^(-1)x+3tan^(-1)x

IF 2 tan ^(-1) (cos x) =tan ^(-1) (2 "cosec"x) then sin x cos x=

f((2tan x)/(1+tan^(2)x))=((cos2x+1)(sec^(2)x+tan x))/(2) then f(x)=