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

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

Prove that: (9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2sqrt(2))/3)

Prove that: sin^(-1)(-4/5)=tan^(-1)(-4/3)=cos^(-1)(-3/5)-pi

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

Prove: sin^(-1)(1/sqrt5)+cot^(-1)3=pi/4

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

Prove that: (9pi)/8-9/4sin^(-1)1/3=9/4sin^(-1)(2sqrt(2))/3

Prove that: sin36^0=(sqrt(10-2sqrt(5)))/4 .

Prove that sin^(-1)(4/5)+tan^(-1)(5/12)+cos^(-1)(63/65)=pi/2

(i) If sin ^(-) x + sin ^(-1) y = pi//2 , then prove that : cos^(-1) x = sin^(-1) y (ii) Prove that : sin ((1)/(2) cos^(-1).(4)/(5))= (1)/sqrt(10) (iii) Prove that : tan ((1)/(2) cos^(-1).(sqrt(5))/(3)) = (3-sqrt(5))/(2)