If an angle A of $∆ A B C$ satisfies $5 C O S A + 3 = 0$ then the roots of the quadratic equation $9 x^{2} + 27 x + 20 = 0$ are

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$S i n A, S e c A$

$S e c A, T a n A$

$T a n A, C o s A$

$S e c A, C o s A$

answer is B.

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Detailed Solution

$G i v e n 5 C o s A + 3 = 0 \Rightarrow C o s A = \frac{- 3}{5}$

$G i v e n e q u a t i o n 9 x^{2} + 27 x + 20 = 0 \Rightarrow 9 x^{2} + 15 x + 12 x + 20 = 0 \Rightarrow 3 x (3 x + 5) + 4 (3 x + 5) = 0 \Rightarrow (3 x + 5) (3 x + 4) = 0 \Rightarrow x = \frac{- 5}{3} = S e c A a n d x = \frac{- 4}{3} = T a n A$

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