The given limit,
=limx→0(1+sinx+sin2x2!+sin3x3!+……….)–(1–sinx+sin2x2!–sin3x3!+……….)–2(x+x33+215x5+……….)(x+x33+215x5+……….)–x
=limx→02(sinx+sin3x3!+sin5x5!+……….)–2(x+x33+215x5+……….)x33+215x5+……….
=limx→02(sinx–x+sin3x3!–x33+sin5x5!–215x5+……….)x33+215x5+……….
=limx→02(x–x33!+x55!–………..–x+sin3x3!–x33+sin5x5!–215x5+……….)x33+215x5+……….
=limx→02(–x33!+x55!–………..+sin3x3!–x33+sin5x5!–215x5+……….)x33+215x5+……….
=limx→02(–13!+x25!–………..+sin3xx33!–13+sin5xx35!–215x2+……….)13+215x2+……….
=2(–13!+13!–13)13=–2