The value of limx→π/4 22−(cosx+sinx)31−sin2x,is
32
23
12
2
We have,
limx→π/4 22−(cosx+sinx)31−sin2x=limx→π/4 23/2−(cosx+sinx)23/22−(1+sin2x)=limx→π/4 23/2−(1+sin2x)3/22−(1+sin2x)
=limy→2 y3/2−23/2y−2,where y=1+sin2x
=32(2)3/2−1=32×2=32