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

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Write down the domain of : (i) f(x) = sin^(-1) x (ii) f(x) = cos^(-1)x (iii) f(x) = tan^(-1)x (iv) f(x) = sec^(-1) x

if 0

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

If -1

(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx

(i) 4cos^(2)x=1 (ii) 4sin^(2)x-3=0 (iii) tan^(2)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 sin^(-1)x_(i)in[0,1]AA i=1,2,3,....28 then find the maximum value of sqrt(sin^(-1)x_(1))sqrt(cos^(-1)x_(2))+sqrt(sin^(-1)x_(2))sqrt(sin^(-1)x_(3))+sqrt(sin^(-1)x_(3))sqrt(cos^(-1)x_(4))+...+sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_(1))