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Trigonometric Ratios of Multiples of an Angle

Find the valu...

Question

Find the value of tan (A + B) if the roots of the equation $6 x^{2} - 5 x + 1 = 0$ are tan A and tan B

A

2

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B

√3

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C

3

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D

1

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Solution

The correct option is D
1

tan A + tan B = $\frac{5}{6}$
tan A tan B = $\frac{1}{6}$
tan(A+B) = $\frac{t a n A + t a n B}{1 - t a n A t a n B}$
$= \frac{\frac{5}{6}}{1 - \frac{1}{6}}$
$= \frac{\frac{5}{6}}{\frac{5}{6}}$
= 1

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