905^(-1)(-(1)/(sqrt(2)))

The matrix A={:[((1)/(sqrt(2)),(1)/(sqrt(2))),((-1)/(sqrt(2)),(-1)/(sqrt(2)))]:} is

The matrix A={:[((1)/(sqrt(2)),(1)/(sqrt(2))),((-1)/(sqrt(2)),(-1)/(sqrt(2)))]:} is

(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))-(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))+(1)/(sqrt(2)+1)-(1)/(sqrt(2)-1)

quad Ifalpha=2tan^(-1)(sqrt(3-2sqrt(2)))+sin^(-1)((1)/(sqrt(6)-sqrt(2))),beta=cot^(-1)(sqrt(3)-2)+(1)/(8)sec^(-1)(-2) and gamma=tan^(-1)((1)/(sqrt(2)))+cos^(-1)((1)/(sqrt(3))), then

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

6 + log_(1/4) (1/sqrt(2))[sqrt(1-(1/sqrt(2))sqrt(1-(1/sqrt(2))sqrt(1-(1/sqrt(2)))]

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

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

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