Let f(x)=sin x +cos x+ tan x+ arc sin x+ arc cos x + arc tan x . If M and m are maximum and minimum values of f(x) , then their arithmetic mean is equal to

Domain of f is [-1,1]fx=sinx+cosx+tanx+sin-1x+cos-1x+tan-1xfx=sinx+cosx+tanx+π2+tan-1xf'x=cosx-sinx+sec2x+0+11+x2 here,sec2≥1 and 11+x2∈12,1 and  cosx-sinx ∈-2,2hence f'x>0⇒ f is increasingRange is [f(-1),f(1)]∴fxmin=f-1=-sin1+cos1-tan1+π2-π4                   m=π4+cos1-sin1-tan1∴fxmax=f1=sin1+cos1+tan1+π2+π4                      M=3π4+cos1+sin1+tan1                       ⇒M+m2=π2+cos1