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Antiderivative

If A+B+C=π ...

Question

If $A + B + C = π$ and cosA=cosB cosC, then tanB tanC is equal to

A

\frac{1}{2}

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B

2

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C

1

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D

- \frac{1}{2}

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Solution

The correct option is D $2$
Given $A + B + C = π ⟹ A = π - (B + C)$
And also given $cos A = cos B cos C$
$⟹ cos (π - (B + C)) = cos B cos C$
$⟹ - cos B cos C + sin B sin C = cos B cos C$
$⟹ sin B sin C = 2 cos B cos C$
$⟹ tan B tan C = 2$

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