sin2x=(2tanx)/[1+tan^2(x)]f(tanx)=(2tanx)/[1+tan^2(x)]f(x)=(2x)/[1+x^2]f(sinx)=(2sinx)/[1+sin^2(x)]f(cosx)=(2cosx)/[1+cos^2(x)](2sinx)/[1+sin^2(x)]>(2cosx)/[1+cos^2(x)](sinx-cosx)(sinx+cosx)^2>0sinx>c...