Mathematics

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

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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Single Correct Medium Published on 09th 09, 2020
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