If `0ltalt1`, prove that `0lta^2ltalt1`

If 0ltthetaltpi, prove that cot\ theta/2ge1+cot theta

If xgt0 prove that x+ 1/x ge2

If 0lta_1lta_2lt....lta_n , then prove that tan^(-1)((a_1x-y) /(x+a_1y))+tan^(-1)((a_2-a_1) /(1+a_2a_1))+tan^(-1)((a_3-a_2)/(1+a_3a_2))+.......+tan^(-1)((a_n-a_(n-1)) /(1+a_n a_(n-1)))+tan^(-1)(1/(a_n))=tan^(-1)(x/y)dot

If sinalphasinbeta-cosalphacosbeta+1=0, then prove that 1+cotalphatanbeta=0

If a+b=1,a >0, prove that (a+1/a)^2+(b+1/b)^2geq(25)/2dot

Prove that ln(1+x) 0.

If x=(sqrt(2a+1)+sqrt(2a-1))/(sqrt(2a+1)-sqrt(2a-1)) , prove that x^(2)-4ax+1=0

If [[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all positive integers ndot

Prove that int_0^1xe^xdx =1

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .