Q60 / 160 · AP EAMCET 2022 (04 Jul Shift 2) · Mathematics

If $A + B + C = π, \cos B = \cos A \cos C$ , then $\tan A \tan C =$

A
$0$
B
$1$
Correct answer
C
$2$
D
$\frac{1}{2}$

Solution

Given,
$A + B + C = π$
Now,
$\cos B = \cos A \cos C$
$\Rightarrow \cos (π - (A + C)) = \cos A \cos C$
$\Rightarrow - \cos (A + C) = \cos A \cos C$
$\Rightarrow \cos A \cos C - \sin A \sin C = - \cos A \cos C$
$\Rightarrow \sin A \sin C = 2 \cos A \cos C$
$\Rightarrow \tan A \tan C = 2$ .

Hence, the correct answer is option: 'C'.

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