Prove that, `2 "sin"^(-1)(2)/(sqrt(13))+(1)/(2) "cos"^(-1)(7)/(25)+"tan"^(-1)(63)/(16)=pi`

Prove that cos^(-1)x=2sin^(-1)(sqrt (1-x)/sqrt2)

Show that sin^(-1) (12/13)+cos^(-1)(4/5)+tan^(-1)(63/16) = pi .

Prove that : "cos"^(-1)sqrt((2)/(3))-"cos"^(-1)(sqrt(6)+1)/(2sqrt(3))=(pi)/(6)

Show that "sin"^(-1)12/13+"cos"^(-1)4/5+"tan"^(-1)63/16=pi

Prove that tan^(-1)((1)/(sqrt(x^(2) -1))) = (pi)/(2) - sec^(-1) x, x gt 1

Prove That : 2"sin"^(-1)3/5="tan"^(-1)24/7

Prove that cot^(-1).(3)/(4) + sin^(-1).(5)/(13) = sin^(-1).(63)/(65)

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/4+(cos^(-1)x)/2,""0 < x < 1

Prove That : "tan"^(-1)63/16="sin"^(-1)5/13+"cos"^(-1)3/5