Let A=sinx+tanx and B=2x in  the  interval 0

We have A=sinx+tanx, B=2xA−B=sinx+tanx−2x                     = sinx−x+tanx−xLet f(x)=sinx−x+tanx−x⇒         f1(x)=cosx−1+sec2x−1                               =cosx−1+tan2x⇒f11(x)=−sinx+2tanxsec2x                             =tanx2sec2x−cosx>0 in 0,π2⇒f1(x) is increasing in 0,π2             ∴x>0⇒f1x>f10               ⇒f1(x)>0           ⇒f(x) is an increasing function in 0,π2           ∴ x>0⇒f(x)>f(0)⇒                      f(x)>0 ⇒            A−B>0⇒A>B