" 6."(i)x tan^(-1)x

If I=inttan^(-1)((2x)/(1-x^(2)))dx, " then ", I-2x tan^(-1)x=

If I=inttan^(-1)((2x)/(1-x^(2)))dx, " then ", I-2x tan^(-1)x=

Prove that i) tan^(-1)(1+x)/(1-x)=pi/4 + tan^(-1)x,x lt 1 ii) tan^(-1)x+cot^(-1)(x+1)=tan^(-1)(x^(2)+x+1)

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

Find the sum of each of the following series: (i) tan^(-1)((1)/(x^(2)+x+1))+tan^(-1)((1)/(x^(2)+3x+3))+tan^(-1)((1)/(x^(2)+5X+7))+tan^(-1)((1)/(x^(2))+7x+13))...... upto n.

Let |{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3x), (tan^(-1)3x, tan^(-1)x, tan^(-1)2x), (tan^(-1)2x, tan^(-1)3x, tan^(-1)x):}|=0 , then the number of values of x satisfying the equation is

If tan^(-1)""(a+x)/a+tan^(-1)""(a-x)/a=pi/6 , then x^(2)=

If tan^(-1)(x+(3)/(x))-tan^(-1)(x-(3)/(x))=tan^(-1)(6)/(x) then the value of x^(4) is

Solve : (i)" "tan^(-1). x/2 +tan^(-1). x/3 = pi/4 , sqrt(6) gt x gt 0 (ii)" "sin(sin^(-1) . 1/5+cos^(-1)x)=1

" (i) "tan( 1/2(tan^(-1)x+tan^(-1)(1/x)))=1