`cot(7(1/2)^(@)=sqrt(p)+sqrt(q)+sqrt(r)+sqrt(s),`

Show that cot (7 (1)/(2)) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6) .

(1)/(sqrt(2)+sqrt(5)-sqrt(7))

(i) (a^(p+q))^(p-q) (a^(q+r))^(q-r)(a^(r+p))^(r-p) (ii) [(a/b)^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r)) [(a/b)^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))

6. Find the positive integers p,q,r, s satisfying tan((pi)/(24))=(sqrt(p)-sqrt(q))(sqrt(r)-(s))

(1)/(sqrt(7)-sqrt(2))-(1)/(sqrt(7)+sqrt(2))=

[((a)/(b))^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[((a)/(b))^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r))[((a)/(b))^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))

If (sqrt(7)+2sqrt(3))/(2sqrt(7)-sqrt(5))=(c+sqrt(p)+sqrt(q)+sqrt(r))/23(p < q < r), where p, q r are rational numbers, then q+ r - p =

Find the positive integers p,q,r, s satisfying tan((pi)/(24))=(sqrt(p)-sqrt(q))(sqrt(r)-s)

6. Find the positive integers p,q,r, s satisfying tan((pi)/(24))=(sqrt(p)-sqrt(q))(sqrt(r)-s)