Find the limit limx→π/4(1−tanxsinx−cosx)
limx→π/4(1−tanxsinx−cosx)=limx→π/4(1−sinxcosxsinx−cosx)=limx→π/4cosx−sinxsinx−cosx(1cosx)=limx→π/4−\cancel(sinx−cosx)\cancel(sinx−cosx)(1cosx)=limx→π/4−1cosx=−1cosπ4=−1√22=−2√2(By rationalizing the denominator)=−2√2⋅√2√2=−\cancel2√2\cancel2=−√2
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