Mathematics

$$\Delta ABC$$ is a right angled at A, the value of tan B $$\times$$ tan C is:


ANSWER

1


SOLUTION
In $$\triangle  ABC$$
$$\angle A+\angle B+\angle C={ 180 }^{ \circ  }\\ \angle B+\angle C={ 180 }^{ \circ  }-{ 90 }^{ \circ  }={ 90 }^{ \circ  }\\ \angle C={ 90 }^{ \circ  }-\angle B$$
$$\tan { B } \times \tan { C } \\ =\tan { B } \times \tan { \left( { 90 }^{ \circ  }-\angle B \right)  } \\ =\tan { B } \times \cot { B } \\ =\tan { B } \times \dfrac { 1 }{ \tan { B }  } \\ =1$$
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