" 5.(i) "2sec^(-1)2x-3sin^(-1)x+cos^(-1)(x^(2))

Find the derivatives w.r.t. x : 2 sec^(-1) 2x-3 sin^(-1)x+cos^(-1)(x^(2))

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 .

int(sin^(2)x*sec^(2)x+2tanx*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx= a) (cos^(2)x)(sin^(-1)x)+C b) (sin^(2)x)(sin^(-1)x)+C c) (sec^(2)x)(cos^(-1)x)+C d) (sec^(2)x)(tan^(-1)x)+C

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

Find the value of x for which the following expression are defined (i) sin^(-1) (3x -2) (ii) cos^(-1) (log_(e) x) (iii) sec^(-1) (x^(2) -2)

Find the value of x for which the following expression are defined (i) sin^(-1) (3x -2) (ii) cos^(-1) (log_(e) x) (iii) sec^(-1) (x^(2) -2)

Find the value of x for which the following expression are defined (i) sin^(-1) (3x -2) (ii) cos^(-1) (log_(e) x) (iii) sec^(-1) (x^(2) -2)

If 0 < cos^(-1)x < 1 and 1+ sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+.....oo=2 then x equals

If sin^(-1)((5)/(x))+sin^(-1)((12)/(x))=sin^(-1)((2)/(x))+cos^(-1)((2)/(x)) then the value of x is equal to

If sin^(-1)((5)/(x))+sin^(-1)((12)/(x))=sin^(-1)((2)/(x))+cos^(-1)((2)/(x)) then the value of x is equal to