First slide

Compound angles

Question

If A, B, C are in A.P and $B = \frac{π}{4}$ then $\tan A \tan B \tan C =$

Moderate

A

1
B

3
C

4
D

0

Solution

$\begin{array}{l} W e h a v e 2 B = A + C a n d B = \frac{π}{4} \\ \Rightarrow \tan 2 B = \frac{\tan A + \tan C}{1 - \tan A \cdot \tan C} \\ B u t \tan 2 B = \tan \frac{π}{2} = n o t d e f i n e d \\ \Rightarrow 1 - \tan A \tan C = 0 \\ \Rightarrow \tan A \tan C = 1 \\ ∴ \tan A \tan B \tan C = 1 (∵ \tan B = \tan \frac{π}{4} = 1) \end{array}$

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