Show that :
`( sqrt(a) - 1/sqrt(a) )^2 = ( a + 1/a - 2 )`

Show that (sqrt(2)+1)^(6)+(sqrt(2)-1)^(6)=198

Evaluate : 1/( 1 + sqrt (2) ) + 1/( sqrt(2) + sqrt (3) ) + 1/ ( sqrt(3) + sqrt (4) )

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(2) .

Show that : cot^(-1) [(sqrt(1 + sinx) + sqrt(1 - sinx))/(sqrt(1 + sinx) - sqrt(1 - sinx))]= x/2

( Show that: )/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

Show that tan pi/16 = sqrt(4 +2 sqrt2) - (sqrt2+1) .

Show that points (2-sqrt3 , sqrt3 +1) , (1,0) and (3,2) form an equilateral triangle .

Show that sin A = sqrt(1-cos^2 A) .

Show that sin A = sqrt(1-cos^2 A) .