Question

$lim sinx - cosx \div x - \pi - \div 4$

Answer 1

sinx−cosxcos2x=sinx−cosxcos2x−sin2x=−cosx−sinx(cosx−sinx)⋅(cosx+sinx)=−1cosx+sinx

Hence the limit is

limx→π4−1cosx+sinx=−1cos45+sin45=−12⋅√22=−1√2sinx−cosxcos2x=sinx−cosxcos2x−sin2x=−cosx−sinx(cosx−sinx)⋅(cosx+sinx)=−1cosx+sinx

Hence the limit is

limx→π4−1cosx+sinx=−1cos45+sin45=−12⋅√22=−1√2