[/_SPT=120^(@)" .Prove that "OP=2PS" ."],[qquad [(sqrt(1)+(1)/(n))^(0)]]

Prove that (sqrt(2)-1)^(2n)

Prove that, lim_(ntooo)(sqrt(1+n+n^(2))-n)=(1)/(2)

Prove that : int_(0)^(1)x(1-x)^(n)dx=1/((n+1)(n+2))

int_(0)^( Prove that )sqrt(1+sec x)dx=sin^(-1)(sqrt(2)sin((x)/(2)))

Prove that tan [7(1)/(2)]^0 = (sqrt(3) - sqrt(2)) (sqrt(2) - 1) .

Prove that : int_0^(pi/2)sqrt(1-sin2x)dx=2(sqrt(2)-1)

From a point P ,two tangents PT and PS are drawn to a circle with center O.Such that /_SPT=120^(@). Prove that OP=2PS.

If f(x) is continuous in [0,1] and f((1)/(2))=1 prove that lim_(n rarr oo)f((sqrt(n))/(2sqrt(n+1)))=1

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

Prove : underset(nrarroo)"lim"(sqrt(n+1)-sqrt(n))=0