Evaluate:Cot75°×Cot30°×Cot15°×Tan77°×Tan13°
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cot(75)×cot(30)×cot(15)×tan(77)×tan(13)=cot(75)×cot(30)× tan(90−15)×tan(77)×cot(90−13)=cot(75)×cot(30)×tan(75)×tan(77)×cot(77)=1×1×cot(30)=cot(30)=3\begin{lgathered}\cot(75) \times \cot(30) \times \cot(15) \times \tan(77) \times \tan(13) \\ = \cot(75) \times \cot(30) \times \ \tan(90 - 15) \times \tan(77) \times \cot(90 - 13) \\ = \cot(75) \times \cot(30) \times \tan(75) \times \tan(77) \times \cot(77) \\ = 1 \times 1 \times \cot(30) \\ = \cot(30 ) = \sqrt{3}\end{lgathered}
cot(75)×cot(30)×cot(15)×tan(77)×tan(13)
=cot(75)×cot(30)× tan(90−15)×tan(77)×cot(90−13)
=cot(75)×cot(30)×tan(75)×tan(77)×cot(77)
=1×1×cot(30)
=cot(30)=
_/3
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