Prove that : `4(sin^(-1)(1/sqrt(10)) + cos^(-1)( 2/sqrt(5)))=pi`

Prove that: i) sin^(-1)(1/sqrt(5))+sin^(-1)(2/sqrt(5))=pi/2

sin^(-1)(1/sqrt5)+cos^(-1)(3/sqrt(10))

sin^(-1)((1)/(sqrt(5)))+sin^(-1)((1)/(sqrt(10)))=(pi)/(4)

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

Prove that: cos36^(@)=(sqrt(5)+1)/(4)

Prove: sin^(-1)((1)/(sqrt(5)))+cot^(-1)3=(pi)/(4)

Prove that cos^(-1) (sqrt(1/3))-cos^(-1) (sqrt((1)/(6)))+cos^(-1) ((sqrt(10)-1)/(3sqrt2))=cos^(-1) (2/3)

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 lt x lt 1