Let h=x−π/4, so x→π/4 means h→0.
Numerator: tan(π/4−x)=tan(−h)=−tanh≈−h.
Denominator: cot(2x)=cot(π/2+2h)=−tan(2h)≈−2h.
Limit =h→0lim−2h−h=21.
So k=1/2.
If f(x)={cot2xtan(π/4−x),k,x=π/4x=π/4 is continuous at x=π/4, then the value of k is
Held on 4 Aug 2022 · Verified 13 Jul 2026.
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