" (i) "[cos^(2)1-x cos alpha],[" (ii) "sec^(-1)(x+1)/(x-1)+sin^(-1)(x-1)/(x+1)]

Prove that i) cos^(-1)(1-2x^(2))=2sin^(-1)x ii) cos^(-1)(2x^(2)-1)=2cos^(-1)x . iii) sec^(-1)(1/(2x^(2)-1)=2cos^(-1)x iv) cot^(-1)(sqrt(1-x^(2))-x)=pi/2-1/2cot^(-1)x .

If sec^(-1)x=cos ec^(-1)y, then cos^(-1)((1)/(x))=cos^(-1)((1)/(y))=

If sec^(-1) x = "cosec" ^(-1) y , then the valuw of cos^(-1) ""(1)/(x) - sin ^(-1)""(1)/(y) will be

{ cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)

int (sin^(-1)x - cos^(-1)x)/(sin^(-1)x + cos^(-1)x)dx =

Find the value of sin^(-1)(2^x) (ii) cos^(-1)sqrt(x^2-x+1) tan^(-1)(x^2)/(1+x^2) (iv) sec^(-1)(x+1/x)

Solve for x : i) cos(sin^(-1)x)=1/2 ii) tan^(-1)x=sin^(-1)1/sqrt(2) iii) sin^(-1)x-cos^(-1)x=pi/6

sec^(-1) x + cosec^(-1) x + cos^(-1) (x^(-1) ) + sin^(-1) ( x^(-1) ) = ….. (where |x| ge 1 , x in R )

Find the value of sin^(-1)x+sin^(-1)(1)/(x)+cos^(-1)x+cos^(-1)(1)/(x)

The domain of f(x) =cos ^(-1) (sec (cos ^(-1) x)) + sin ^(-1) ( cosec( sin ^(-1) x)) is