How do I show that sinx + tanx > 2x if 0 < x < pi/2 ?
Both functions are non negative on the specified interval. The derivative of 2x is 2 while the derivative of sin(x) + tan(x) = cos(x)+1/cos(x)^2 which is clearly greater than or equal to 2. Since sin(x)+tan(x) = 2x at x=0 and sin(x)+tan(x) is increasing faster than 2x for every value of x (0,pi/2], sin(x)+tan(x) is greater than or equal to 2x.