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`

Solve: sin^(-1)x-cos^(-1)x = pi/6

Solve: sin^(-1)x=pi/6+cos^(-1)x

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

Solve : sin ^(-1)x - cos ^(-1) x = (pi )/(6)

prove that sin^(-1) cos sin^(-1)x + cos^(-1) sin cos^(-1)x = pi /2

Solve : cos^(-1) (sin cos^(-1)x ) =(pi)/(6) .

Solve the following equations: sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^(-1)x sin^(-1)6x+sin^(-1)6sqrt(3)x=pi/2

Solve: "cos"^(-1) x +"sin"^(-1) x/2= pi/6

Solve : cos ^(-1) x + sin ^(-1) "" (x)/( 2) = (pi)/(6)

Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^(-1)(sin x/(1+cos x)) (iii) sin ^(-1)((2^(x+1))/(1+4^x))