In a right angled triangle ABC (right angled at B)

The value of tan A tan C=__

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Solution

From figure, tan A= $\frac{B C}{A B}$

and tan C = $\frac{A B}{B C}$

So, tan A tan C= $\frac{B C}{A B} \times \frac{A B}{B C} = 1.$

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