Question

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

• A. $0$
• B. $1$
• C. $-1$
• D. None of the above

Answer 1

The correct option is B $1$

In $△ABC$, by angle sum property,

$\angle A+\angle B+\angle C={180}^{\circ }$

${90}^o+\angle B+\angle C={180}^{\circ }$

$⟹$ $\angle B+\angle C={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

$⟹$$\angle C={90}^{\circ }-\angle B$.

Then,

$\tan B\times \tan C$

$=\tan B\times \tan ({90}^{\circ }-\angle B)$

$=\tan B\times \cot B=\tan B\times \frac{1}{\tan B}=1$.

Therefore, option $B$ is correct.